{"id":244,"date":"2023-06-08T14:36:27","date_gmt":"2023-06-08T14:36:27","guid":{"rendered":"https:\/\/ilm.com.pk\/online-test\/?p=244"},"modified":"2023-06-08T09:29:59","modified_gmt":"2023-06-08T09:29:59","slug":"2nd-year-math-chapter-2-differentiation-mcqs-with-answers","status":"publish","type":"post","link":"https:\/\/ilm.com.pk\/online-test\/2nd-year-math-chapter-2-differentiation-mcqs-with-answers\/","title":{"rendered":"2nd Year Math Chapter 2 Differentiation MCQs With Answers"},"content":{"rendered":"<p style=\"text-align: justify;\">Your search for the 2nd Year Math Chapter 2 Differentiation MCQs With Answers is going to end here. This place is where you will find the important MCQs of Differentiation. This chapter consists of the concepts including Dependent and Independent Variables and Derivation of function. After this, you will be able to get the concept of finding f'(x) from the definition of the derivative. There are some important theorems of differentiation. Through these MCQs, you can improve the concepts including the chain rule, the derivative of inverse functions, the differentiation of implicit relations, trigonometric functions, and inverse trigonometric functions. So, these are Important topics and you will get the 2nd Year Math MCQs with Answers Chapter 2 here. Scroll down and get the resources.<\/p>\n<h2 style=\"text-align: center;\">2nd Year Math Chapter 2 Differentiation MCQs With Answers<\/h2>\n<div class='ays-quiz-wrap'>\n            <div class='ays-quiz-container ays_quiz_elegant_light  '\n                 data-quest-effect='shake' \n                 data-hide-bg-image='false'\n                 id='ays-quiz-container-74'>\n                <div class='ays-live-bar-wrap '><div class='ays-live-bar-fill ' style='width: 0%;'><span><span class='ays-live-bar-percent'>0<\/span>%<\/span><\/div><\/div>\n                \n                <div class='ays-questions-container'>\n                    <div class='ays-quiz-some-items-icons-wrap'><\/div>\n                    <span class='ays_quizn_ancnoxneri_qanak'><i class='ays_fa ays_fa_users'><\/i> 879<\/span>\n                    <div id='ays-quiz-questions-nav-wrap-74' class='ays-quiz-questions-nav-wrap'><div class='ays-quiz-questions-nav-go-left'>\n                    <i class='ays_fa ays_fa_angle_left'><\/i>\n                <\/div><div class='ays-quiz-questions-nav-go-right'>\n                    <i class='ays_fa ays_fa_angle_right'><\/i>\n                <\/div><div class='ays-quiz-questions-nav-content'><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1541' class='ays_questions_nav_question'>1<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1540' class='ays_questions_nav_question'>2<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1535' class='ays_questions_nav_question'>3<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1529' class='ays_questions_nav_question'>4<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1532' class='ays_questions_nav_question'>5<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1527' class='ays_questions_nav_question'>6<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1539' class='ays_questions_nav_question'>7<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1530' class='ays_questions_nav_question'>8<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1524' class='ays_questions_nav_question'>9<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1528' class='ays_questions_nav_question'>10<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1538' class='ays_questions_nav_question'>11<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1537' class='ays_questions_nav_question'>12<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1536' class='ays_questions_nav_question'>13<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1525' class='ays_questions_nav_question'>14<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1534' class='ays_questions_nav_question'>15<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1542' class='ays_questions_nav_question'>16<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1533' class='ays_questions_nav_question'>17<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1531' class='ays_questions_nav_question'>18<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1543' class='ays_questions_nav_question'>19<\/a><\/div><div class='ays-quiz-questions-nav-item'><a href='javascript:void(0);' data-id='1526' class='ays_questions_nav_question'>20<\/a><\/div><\/div><\/div>\n                    <form \n                        action='' \n                        method='post' \n                        autocomplete='off'\n                        id='ays_finish_quiz_74' \n                        class=' enable_questions_result '\n                    >\n            <input type='hidden' value='list' class='answer_view_class'>\n            <input type='hidden' value='' class='ays_qm_enable_arrows'><section  style='display:none;'  class='ays_quiz_timer_container'>\n                <div class='ays-quiz-timer ' data-timer='100'><\/div>\n                <div class='ays-quiz-after-timer  empty_after_timer_text '><\/div>\n                <hr style='height:1px;'>\n            <\/section>\n            \n            <div class='step active-step'>\n                <div class='ays-abs-fs ays-start-page'>\n                    \n                    \n                    <p class='ays-fs-title'>2nd Year Math Chapter 2<\/p>\n                    \n                    <input type='hidden' name='ays_quiz_id' value='74'\/>\n                    <input type='hidden' name='ays_quiz_questions' value='1543,1542,1541,1540,1539,1538,1537,1536,1535,1534,1533,1532,1531,1529,1530,1528,1527,1526,1525,1524'>\n                    \n                    <div class='ays_buttons_div'>\n                        <input type='button'   name='next' class='ays_next start_button action-button' value='Start' data-enable-leave-page=\"false\" \/>\n                    <\/div>\n                    \n                    \n                <\/div>\n            <\/div><div class='step  '\n                        data-question-id='1541'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>1 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>1. <strong>If y = e\u2212ax , then y2 =<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1541]' id='ays-answer-5956-74' value='5956'\/>\n\n                    <label for='ays-answer-5956-74' class='  ays_position_initial '>\n                        A) \u2013 a^2 e^ax\n                    <\/label>\n                    <label for='ays-answer-5956-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1541]' id='ays-answer-5958-74' value='5958'\/>\n\n                    <label for='ays-answer-5958-74' class='  ays_position_initial '>\n                        B) \u2013 a^2 e^\u22122ax\n                    <\/label>\n                    <label for='ays-answer-5958-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1541]' id='ays-answer-5957-74' value='5957'\/>\n\n                    <label for='ays-answer-5957-74' class='  ays_position_initial '>\n                        C) a^2 e^\u22122ax\n                    <\/label>\n                    <label for='ays-answer-5957-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1541]' id='ays-answer-5955-74' value='5955'\/>\n\n                    <label for='ays-answer-5955-74' class='  ays_position_initial '>\n                        D) \u2013 ae^ax\n                    <\/label>\n                    <label for='ays-answer-5955-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1540'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>2 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>2. <strong>y = sech<sup>\u22121<\/sup>x if and only if x = sechy is valid when<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1540]' id='ays-answer-5951-74' value='5951'\/>\n\n                    <label for='ays-answer-5951-74' class='  ays_position_initial '>\n                        A) x \u2208 R, y \u2208 R \u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5951-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1540]' id='ays-answer-5954-74' value='5954'\/>\n\n                    <label for='ays-answer-5954-74' class='  ays_position_initial '>\n                        B) x \u2208 (0,1], y \u2208 [0, \u221e)\n                    <\/label>\n                    <label for='ays-answer-5954-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1540]' id='ays-answer-5952-74' value='5952'\/>\n\n                    <label for='ays-answer-5952-74' class='  ays_position_initial '>\n                        C) x \u2208[ \u2212 1,1], y \u2208 R\n                    <\/label>\n                    <label for='ays-answer-5952-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1540]' id='ays-answer-5953-74' value='5953'\/>\n\n                    <label for='ays-answer-5953-74' class='  ays_position_initial '>\n                        D) x \u2208 [\u22121,1], y \u2208 R \u2212 {0}\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5953-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1535'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>3 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>3. <strong>d\/dx [f(x) + g(x)] =<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1535]' id='ays-answer-5932-74' value='5932'\/>\n\n                    <label for='ays-answer-5932-74' class='  ays_position_initial '>\n                        A) f\u2032(x) \u2212 g\u2032(x)\n                    <\/label>\n                    <label for='ays-answer-5932-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1535]' id='ays-answer-5931-74' value='5931'\/>\n\n                    <label for='ays-answer-5931-74' class='  ays_position_initial '>\n                        B) f\u2032 (x) + g\u2032 (x)\n                    <\/label>\n                    <label for='ays-answer-5931-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1535]' id='ays-answer-5933-74' value='5933'\/>\n\n                    <label for='ays-answer-5933-74' class='  ays_position_initial '>\n                        C) f(x)g\u2032(x) + g(x)f\u2032(x) \u00a0\n                    <\/label>\n                    <label for='ays-answer-5933-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1535]' id='ays-answer-5934-74' value='5934'\/>\n\n                    <label for='ays-answer-5934-74' class='  ays_position_initial '>\n                        D) f(x)g\u2032(x) \u2212 g(x)f\u2032(x)\n                    <\/label>\n                    <label for='ays-answer-5934-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1529'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>4 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>4. The notation dy\/dx or df\/dx is used by<\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1529]' id='ays-answer-5908-74' value='5908'\/>\n\n                    <label for='ays-answer-5908-74' class='  ays_position_initial '>\n                        A) Newton\n                    <\/label>\n                    <label for='ays-answer-5908-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1529]' id='ays-answer-5909-74' value='5909'\/>\n\n                    <label for='ays-answer-5909-74' class='  ays_position_initial '>\n                        B) Lagrange\n                    <\/label>\n                    <label for='ays-answer-5909-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1529]' id='ays-answer-5907-74' value='5907'\/>\n\n                    <label for='ays-answer-5907-74' class='  ays_position_initial '>\n                        C) Leibnitz\n                    <\/label>\n                    <label for='ays-answer-5907-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1529]' id='ays-answer-5910-74' value='5910'\/>\n\n                    <label for='ays-answer-5910-74' class='  ays_position_initial '>\n                        D) Cauchy\n                    <\/label>\n                    <label for='ays-answer-5910-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1532'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>5 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>5. <strong>d\/dx(x<sup>n<\/sup>) = nx<sup>n\u22121<\/sup> is called<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1532]' id='ays-answer-5922-74' value='5922'\/>\n\n                    <label for='ays-answer-5922-74' class='  ays_position_initial '>\n                        A) Constant rule\n                    <\/label>\n                    <label for='ays-answer-5922-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1532]' id='ays-answer-5921-74' value='5921'\/>\n\n                    <label for='ays-answer-5921-74' class='  ays_position_initial '>\n                        B) Quotient rule\n                    <\/label>\n                    <label for='ays-answer-5921-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1532]' id='ays-answer-5920-74' value='5920'\/>\n\n                    <label for='ays-answer-5920-74' class='  ays_position_initial '>\n                        C) Product rule\n                    <\/label>\n                    <label for='ays-answer-5920-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1532]' id='ays-answer-5919-74' value='5919'\/>\n\n                    <label for='ays-answer-5919-74' class='  ays_position_initial '>\n                        D) Power rule\n                    <\/label>\n                    <label for='ays-answer-5919-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1527'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>6 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>6. <strong>d\/dx (ax + b)<sup>n<\/sup> =<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1527]' id='ays-answer-5902-74' value='5902'\/>\n\n                    <label for='ays-answer-5902-74' class='  ays_position_initial '>\n                        A) na(ax + b) ^n\u22121\n                    <\/label>\n                    <label for='ays-answer-5902-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1527]' id='ays-answer-5900-74' value='5900'\/>\n\n                    <label for='ays-answer-5900-74' class='  ays_position_initial '>\n                        B) n(a^x + b)^ n\u22121\n                    <\/label>\n                    <label for='ays-answer-5900-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1527]' id='ays-answer-5901-74' value='5901'\/>\n\n                    <label for='ays-answer-5901-74' class='  ays_position_initial '>\n                        C) n(a^n\u22121x)\n                    <\/label>\n                    <label for='ays-answer-5901-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1527]' id='ays-answer-5899-74' value='5899'\/>\n\n                    <label for='ays-answer-5899-74' class='  ays_position_initial '>\n                        D) n(a^n\u22121x + b)\n                    <\/label>\n                    <label for='ays-answer-5899-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1539'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>7 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>7. <strong>y = coth<sup>\u22121<\/sup>x if and only if x = cothy is valid when<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1539]' id='ays-answer-5949-74' value='5949'\/>\n\n                    <label for='ays-answer-5949-74' class='  ays_position_initial '>\n                        A) x \u2208 [\u22121,1], y \u2208 R \u2212 {0}\n                    <\/label>\n                    <label for='ays-answer-5949-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1539]' id='ays-answer-5948-74' value='5948'\/>\n\n                    <label for='ays-answer-5948-74' class='  ays_position_initial '>\n                        B) x \u2208[ \u2212 1,1], y \u2208 R \u00a0\n                    <\/label>\n                    <label for='ays-answer-5948-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1539]' id='ays-answer-5950-74' value='5950'\/>\n\n                    <label for='ays-answer-5950-74' class='  ays_position_initial '>\n                        C) x > 0, y > 0\n                    <\/label>\n                    <label for='ays-answer-5950-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1539]' id='ays-answer-5947-74' value='5947'\/>\n\n                    <label for='ays-answer-5947-74' class='  ays_position_initial '>\n                        D) x \u2208 R, y \u2208 R\n                    <\/label>\n                    <label for='ays-answer-5947-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1530'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>8 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>8. <strong>The notation \u1e1f(x) is used by<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1530]' id='ays-answer-5914-74' value='5914'\/>\n\n                    <label for='ays-answer-5914-74' class='  ays_position_initial '>\n                        A) Cauchy\n                    <\/label>\n                    <label for='ays-answer-5914-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1530]' id='ays-answer-5913-74' value='5913'\/>\n\n                    <label for='ays-answer-5913-74' class='  ays_position_initial '>\n                        B) Lagrange\n                    <\/label>\n                    <label for='ays-answer-5913-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1530]' id='ays-answer-5911-74' value='5911'\/>\n\n                    <label for='ays-answer-5911-74' class='  ays_position_initial '>\n                        C) Leibnitz\n                    <\/label>\n                    <label for='ays-answer-5911-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1530]' id='ays-answer-5912-74' value='5912'\/>\n\n                    <label for='ays-answer-5912-74' class='  ays_position_initial '>\n                        D) Newton\n                    <\/label>\n                    <label for='ays-answer-5912-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1524'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>9 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>9. <strong>d\/dx tan3x =<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1524]' id='ays-answer-5887-74' value='5887'\/>\n\n                    <label for='ays-answer-5887-74' class='  ays_position_initial '>\n                        A) 3 sec2 3x\n                    <\/label>\n                    <label for='ays-answer-5887-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1524]' id='ays-answer-5890-74' value='5890'\/>\n\n                    <label for='ays-answer-5890-74' class='  ays_position_initial '>\n                        B) sec^2 x\n                    <\/label>\n                    <label for='ays-answer-5890-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1524]' id='ays-answer-5888-74' value='5888'\/>\n\n                    <label for='ays-answer-5888-74' class='  ays_position_initial '>\n                        C) 1\/3 sec^2 3x\n                    <\/label>\n                    <label for='ays-answer-5888-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1524]' id='ays-answer-5889-74' value='5889'\/>\n\n                    <label for='ays-answer-5889-74' class='  ays_position_initial '>\n                        D) cot3x\n                    <\/label>\n                    <label for='ays-answer-5889-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1528'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>10 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>10. <strong>The change in variable x is called the increment of x. It is denoted by \u03b4x which is<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1528]' id='ays-answer-5906-74' value='5906'\/>\n\n                    <label for='ays-answer-5906-74' class='  ays_position_initial '>\n                        A) None of these\n                    <\/label>\n                    <label for='ays-answer-5906-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1528]' id='ays-answer-5905-74' value='5905'\/>\n\n                    <label for='ays-answer-5905-74' class='  ays_position_initial '>\n                        B) +iv or \u2013iv\n                    <\/label>\n                    <label for='ays-answer-5905-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1528]' id='ays-answer-5903-74' value='5903'\/>\n\n                    <label for='ays-answer-5903-74' class='  ays_position_initial '>\n                        C) +iv only\n                    <\/label>\n                    <label for='ays-answer-5903-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1528]' id='ays-answer-5904-74' value='5904'\/>\n\n                    <label for='ays-answer-5904-74' class='  ays_position_initial '>\n                        D) \u2013iv only\n                    <\/label>\n                    <label for='ays-answer-5904-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1538'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>11 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>11. <strong>y = tanh<sup>\u22121<\/sup>x if and only if x = tanhy is valid when<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1538]' id='ays-answer-5943-74' value='5943'\/>\n\n                    <label for='ays-answer-5943-74' class='  ays_position_initial '>\n                        A) x \u2208 R, y \u2208 R\u00a0\n                    <\/label>\n                    <label for='ays-answer-5943-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1538]' id='ays-answer-5946-74' value='5946'\/>\n\n                    <label for='ays-answer-5946-74' class='  ays_position_initial '>\n                        B) x > 0, y >0\n                    <\/label>\n                    <label for='ays-answer-5946-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1538]' id='ays-answer-5944-74' value='5944'\/>\n\n                    <label for='ays-answer-5944-74' class='  ays_position_initial '>\n                        C) x \u2208[\u2212 1,1], y \u2208 R\n                    <\/label>\n                    <label for='ays-answer-5944-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1538]' id='ays-answer-5945-74' value='5945'\/>\n\n                    <label for='ays-answer-5945-74' class='  ays_position_initial '>\n                        D) x \u2208 R[\u22121,1], y \u2208 R\u00a0\n                    <\/label>\n                    <label for='ays-answer-5945-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1537'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>12 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>12. <strong>y = cosh<sup>\u22121<\/sup>x if and only if x = coshy is valid when<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1537]' id='ays-answer-5940-74' value='5940'\/>\n\n                    <label for='ays-answer-5940-74' class='  ays_position_initial '>\n                        A) x \u2208 [1, \u221e), y \u2208 (0, \u221e]\u00a0\u00a0\u00a0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5940-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1537]' id='ays-answer-5942-74' value='5942'\/>\n\n                    <label for='ays-answer-5942-74' class='  ays_position_initial '>\n                        B) x \u2208 R, y \u2208 R\n                    <\/label>\n                    <label for='ays-answer-5942-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1537]' id='ays-answer-5939-74' value='5939'\/>\n\n                    <label for='ays-answer-5939-74' class='  ays_position_initial '>\n                        C) x \u2208 [1, \u221e), y \u2208 [0, \u221e)\n                    <\/label>\n                    <label for='ays-answer-5939-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1537]' id='ays-answer-5941-74' value='5941'\/>\n\n                    <label for='ays-answer-5941-74' class='  ays_position_initial '>\n                        D) x < 0, y < 0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5941-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1536'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>13 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>13. <strong>y = sinh<sup>\u22121<\/sup>x if and only if x = sinhy is valid when<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1536]' id='ays-answer-5938-74' value='5938'\/>\n\n                    <label for='ays-answer-5938-74' class='  ays_position_initial '>\n                        A) x \u2208 R, x > 0\n                    <\/label>\n                    <label for='ays-answer-5938-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1536]' id='ays-answer-5937-74' value='5937'\/>\n\n                    <label for='ays-answer-5937-74' class='  ays_position_initial '>\n                        B) x \u2208 R, y > 0\n                    <\/label>\n                    <label for='ays-answer-5937-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1536]' id='ays-answer-5936-74' value='5936'\/>\n\n                    <label for='ays-answer-5936-74' class='  ays_position_initial '>\n                        C) x < 0, y < 0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5936-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1536]' id='ays-answer-5935-74' value='5935'\/>\n\n                    <label for='ays-answer-5935-74' class='  ays_position_initial '>\n                        D) x > 0, y > 0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5935-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1525'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>14 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>14. <strong>d\/dx 2<sup>x<\/sup> =<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1525]' id='ays-answer-5892-74' value='5892'\/>\n\n                    <label for='ays-answer-5892-74' class='  ays_position_initial '>\n                        A) ln2\/2^x\n                    <\/label>\n                    <label for='ays-answer-5892-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1525]' id='ays-answer-5893-74' value='5893'\/>\n\n                    <label for='ays-answer-5893-74' class='  ays_position_initial '>\n                        B) 2^x ln2\n                    <\/label>\n                    <label for='ays-answer-5893-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1525]' id='ays-answer-5891-74' value='5891'\/>\n\n                    <label for='ays-answer-5891-74' class='  ays_position_initial '>\n                        C) 2^x ln2 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5891-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1525]' id='ays-answer-5894-74' value='5894'\/>\n\n                    <label for='ays-answer-5894-74' class='  ays_position_initial '>\n                        D) 2^x\n                    <\/label>\n                    <label for='ays-answer-5894-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1534'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>15 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>15. <strong>d\/dx (Sina) =<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1534]' id='ays-answer-5927-74' value='5927'\/>\n\n                    <label for='ays-answer-5927-74' class='  ays_position_initial '>\n                        A) cos a\n                    <\/label>\n                    <label for='ays-answer-5927-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1534]' id='ays-answer-5930-74' value='5930'\/>\n\n                    <label for='ays-answer-5930-74' class='  ays_position_initial '>\n                        B) \u2013 a cos a\n                    <\/label>\n                    <label for='ays-answer-5930-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1534]' id='ays-answer-5928-74' value='5928'\/>\n\n                    <label for='ays-answer-5928-74' class='  ays_position_initial '>\n                        C) a cos a\n                    <\/label>\n                    <label for='ays-answer-5928-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1534]' id='ays-answer-5929-74' value='5929'\/>\n\n                    <label for='ays-answer-5929-74' class='  ays_position_initial '>\n                        D) 0\n                    <\/label>\n                    <label for='ays-answer-5929-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1542'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>16 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>16. <strong>If a function f is increasing within [a, b] ,then slope of tangent to its graph within [a, b] remains<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1542]' id='ays-answer-5961-74' value='5961'\/>\n\n                    <label for='ays-answer-5961-74' class='  ays_position_initial '>\n                        A) Zero\n                    <\/label>\n                    <label for='ays-answer-5961-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1542]' id='ays-answer-5959-74' value='5959'\/>\n\n                    <label for='ays-answer-5959-74' class='  ays_position_initial '>\n                        B) Positive\n                    <\/label>\n                    <label for='ays-answer-5959-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1542]' id='ays-answer-5960-74' value='5960'\/>\n\n                    <label for='ays-answer-5960-74' class='  ays_position_initial '>\n                        C) Negative\n                    <\/label>\n                    <label for='ays-answer-5960-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1542]' id='ays-answer-5962-74' value='5962'\/>\n\n                    <label for='ays-answer-5962-74' class='  ays_position_initial '>\n                        D) Undefined\n                    <\/label>\n                    <label for='ays-answer-5962-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1533'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>17 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>17. <strong>d\/dx (ax + b)<sup>n<\/sup> = na(ax + b)<sup>n\u22121<\/sup> is valid only when n must be:<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1533]' id='ays-answer-5923-74' value='5923'\/>\n\n                    <label for='ays-answer-5923-74' class='  ays_position_initial '>\n                        A) real number\n                    <\/label>\n                    <label for='ays-answer-5923-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1533]' id='ays-answer-5925-74' value='5925'\/>\n\n                    <label for='ays-answer-5925-74' class='  ays_position_initial '>\n                        B) imaginary number\n                    <\/label>\n                    <label for='ays-answer-5925-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1533]' id='ays-answer-5924-74' value='5924'\/>\n\n                    <label for='ays-answer-5924-74' class='  ays_position_initial '>\n                        C) rational number\n                    <\/label>\n                    <label for='ays-answer-5924-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1533]' id='ays-answer-5926-74' value='5926'\/>\n\n                    <label for='ays-answer-5926-74' class='  ays_position_initial '>\n                        D) Irrational number\n                    <\/label>\n                    <label for='ays-answer-5926-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1531'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>18 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>18. <strong>limx\u2192a f(x)\u2212f(a)\/x\u2212a =<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1531]' id='ays-answer-5916-74' value='5916'\/>\n\n                    <label for='ays-answer-5916-74' class='  ays_position_initial '>\n                        A) f\u2032(a) \u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5916-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1531]' id='ays-answer-5918-74' value='5918'\/>\n\n                    <label for='ays-answer-5918-74' class='  ays_position_initial '>\n                        B) f(x \u2212 a)\n                    <\/label>\n                    <label for='ays-answer-5918-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1531]' id='ays-answer-5917-74' value='5917'\/>\n\n                    <label for='ays-answer-5917-74' class='  ays_position_initial '>\n                        C) f(0)\n                    <\/label>\n                    <label for='ays-answer-5917-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1531]' id='ays-answer-5915-74' value='5915'\/>\n\n                    <label for='ays-answer-5915-74' class='  ays_position_initial '>\n                        D) f\u2032(x)\u00a0\n                    <\/label>\n                    <label for='ays-answer-5915-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1543'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>19 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>19. <strong>If a function f is increasing within [a, b] ,then slope of tangent to its graph within [a, b] remains<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1543]' id='ays-answer-5965-74' value='5965'\/>\n\n                    <label for='ays-answer-5965-74' class='  ays_position_initial '>\n                        A) Zero\n                    <\/label>\n                    <label for='ays-answer-5965-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1543]' id='ays-answer-5966-74' value='5966'\/>\n\n                    <label for='ays-answer-5966-74' class='  ays_position_initial '>\n                        B) Undefined\n                    <\/label>\n                    <label for='ays-answer-5966-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1543]' id='ays-answer-5964-74' value='5964'\/>\n\n                    <label for='ays-answer-5964-74' class='  ays_position_initial '>\n                        C) Negative\n                    <\/label>\n                    <label for='ays-answer-5964-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1543]' id='ays-answer-5963-74' value='5963'\/>\n\n                    <label for='ays-answer-5963-74' class='  ays_position_initial '>\n                        D) Positive\n                    <\/label>\n                    <label for='ays-answer-5963-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_previous action-button ' value='Prev' \/>\n                        \n                        <i class=\"ays_fa ays_fa_arrow_right ays_next action-button ays_arrow ays_next_arrow ays_display_none\"><\/i>\n                        <input type='button' name='next' class='ays_next action-button ' value='Next' \/>\n                    <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step  '\n                        data-question-id='1526'\n                        data-type='radio'\n                        data-required='false'>\n                        \n                        <p class='ays-question-counter animated'>20 \/ 20<\/p>\n                        <div class='ays-abs-fs'>\n                            \n                            <div class='ays_quiz_question'>\n                                <p>20. <strong>If y = e<sup>2x<\/sup>, then y2=<\/strong><\/p>\n\n                            <\/div>\n                            \n                            <div class='ays-quiz-answers ays_list_view_container  '>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1526]' id='ays-answer-5896-74' value='5896'\/>\n\n                    <label for='ays-answer-5896-74' class='  ays_position_initial '>\n                        A) 2e^2x\n                    <\/label>\n                    <label for='ays-answer-5896-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1526]' id='ays-answer-5898-74' value='5898'\/>\n\n                    <label for='ays-answer-5898-74' class='  ays_position_initial '>\n                        B) 16 e^2x\n                    <\/label>\n                    <label for='ays-answer-5898-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='0'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1526]' id='ays-answer-5895-74' value='5895'\/>\n\n                    <label for='ays-answer-5895-74' class='  ays_position_initial '>\n                        C) e^2x\n                    <\/label>\n                    <label for='ays-answer-5895-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div>\n            <div class='ays-field ays_list_view_item'>\n                <input type='hidden' name='ays_answer_correct[]' value='1'\/>\n\n                <input type='radio' name='ays_questions[ays-question-1526]' id='ays-answer-5897-74' value='5897'\/>\n\n                    <label for='ays-answer-5897-74' class='  ays_position_initial '>\n                        D) 4 e^2x \u00a0\u00a0\n                    <\/label>\n                    <label for='ays-answer-5897-74' class='ays_answer_image ays_empty_before_content'><\/label>\n\n                    \n            <\/div><\/div>\n                            \n                            \n                            <div class='ays_buttons_div'>\n                            \n                            <i class=\"ays_fa ays_fa_arrow_left ays_previous action-button ays_arrow ays_display_none\"><\/i>\n                            <input type='button' name='next' class='ays_previous action-button '  value='Prev' \/>\n                            <i class='ays_display_none ays_fa ays_fa_arrow_right ays_finish action-button ays_arrow ays_next_arrow'><\/i><input type='button' name='next' class='  ays_next action-button' value='Finish' \/>\n                        <\/div>\n                            \n                            <div class='wrong_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='right_answer_text ays_do_not_show' style='display:none'>\n                                \n                            <\/div>\n                            <div class='ays_questtion_explanation' style='display:none'>\n                                \n                            <\/div>\n                            \n                        <\/div>\n                    <\/div><div class='step'>\n                    <div class='ays-abs-fs ays-end-page information_form'>\n                    <div class='ays-form-title'><\/div>\n                        <input id='ays_form_field_ays_user_name_74' type='hidden' class='ays_quiz_form_input ays_animated_x5ms' name='ays_user_name' placeholder='Name' \/><input id='ays_form_field_ays_user_email_74' type='hidden' class='ays_quiz_form_input ays_animated_x5ms' name='ays_user_email' placeholder='Email' \/><input id='ays_form_field_ays_user_phone_74' type='hidden' class='ays_quiz_form_input ays_animated_x5ms' name='ays_user_phone' placeholder='Phone Number' \/>\n                        <div class='ays_buttons_div'>\n                            <i class='ays_display_none ays_fa ays_fa_flag_checkered ays_finish action-button ays_arrow ays_next_arrow'><\/i>\n                            <input type='submit' name='ays_finish_quiz' class=' ays_next ays_finish action-button' value='See Result'\/>\n                        <\/div>\n                    <\/div>\n                  <\/div><div class='step ays_thank_you_fs'>\n            <div class='ays-abs-fs ays-end-page'>\n            <div style='text-align:center;'><div data-class='lds-ellipsis' data-role='loader' class='ays-loader'><div><\/div><div><\/div><div><\/div><div><\/div><\/div><\/div><div class='ays_quiz_results_page'><div class='ays_score_message'><\/div><div class='ays_message'><\/div><p class='ays_score ays_score_display_none animated'>Your score is <\/p><div class='ays-progress first'>\n                <span class='ays-progress-value first'>0%<\/span>\n                <div class='ays-progress-bg first'>\n                    <div class='ays-progress-bar first' style='width:0%;'><\/div>\n                <\/div>\n            <\/div><p class='ays_restart_button_p'><button type='button' class='action-button ays_restart_button'>\n                    <i class='ays_fa ays_fa_undo'><\/i>\n                    <span>Restart quiz<\/span>\n                <\/button><\/p><\/div><\/div><\/div><style> div#ays-quiz-container-74 * { box-sizing: border-box; } \/* Styles for Internet Explorer start *\/ #ays-quiz-container-74 #ays_finish_quiz_74 { } \/* Styles for Quiz container *\/ #ays-quiz-container-74{ min-height: 350px; width:100%; background-color:#f2f2f2; background-position:center center;border-radius:0px 0px 0px 0px;box-shadow: 0px 0px 15px 1px rgba(0,0,0,0.4);border-width: 1px;border-style: solid;border-color: #2fa0ca;} \/* Styles for Navigation bar *\/ #ays-quiz-questions-nav-wrap-74 { width: 100%;border-radius:0px 0px 0px 0px;box-shadow: 0px 0px 15px 1px rgba(0,0,0,0.4);border-width: 1px;border-style: solid;border-color: #2fa0ca;} #ays-quiz-questions-nav-wrap-74 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item a.ays_questions_nav_question { color: #000000; border-color: #000000; background-color: #f2f2f2; } #ays-quiz-questions-nav-wrap-74 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item.ays-quiz-questions-nav-item-active a.ays_questions_nav_question { box-shadow: inset 0 0 5px #000000, 0 0 5px #000000; } #ays-quiz-questions-nav-wrap-74 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item.ays-quiz-questions-nav-item-answered a.ays_questions_nav_question { color: #f2f2f2; border-color: #f2f2f2; background-color: #000000; } #ays-quiz-questions-nav-wrap-74 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item a.ays_questions_nav_question.ays_quiz_correct_answer { color: rgba(39, 174, 96, 1); border-color: rgba(39, 174, 96, 1); background-color: rgba(39, 174, 96, 0.4); } #ays-quiz-questions-nav-wrap-74 .ays-quiz-questions-nav-content .ays-quiz-questions-nav-item a.ays_questions_nav_question.ays_quiz_wrong_answer { color: rgba(243, 134, 129, 1); border-color: rgba(243, 134, 129, 1); background-color: rgba(243, 134, 129, 0.4); } \/* Styles for questions *\/ #ays-quiz-container-74 #ays_finish_quiz_74 div.step { min-height: 350px; } \/* Styles for text inside quiz container *\/ #ays-quiz-container-74.ays-quiz-container .ays-questions-container .ays-start-page *:not(input), #ays-quiz-container-74.ays-quiz-container .ays-questions-container .ays_question_hint, #ays-quiz-container-74.ays-quiz-container .ays-questions-container label[for^=\"ays-answer-\"], #ays-quiz-container-74.ays-quiz-container .ays-questions-container p, #ays-quiz-container-74.ays-quiz-container .ays-questions-container .ays-fs-title, #ays-quiz-container-74.ays-quiz-container .ays-questions-container .ays-fs-subtitle, #ays-quiz-container-74.ays-quiz-container .ays-questions-container .logged_in_message, #ays-quiz-container-74.ays-quiz-container .ays-questions-container .ays-quiz-limitation-count-of-takers, #ays-quiz-container-74.ays-quiz-container .ays-questions-container .ays-quiz-limitation-count-of-takers *, #ays-quiz-container-74.ays-quiz-container .ays-questions-container .ays_score_message, #ays-quiz-container-74.ays-quiz-container .ays-questions-container .ays_message{ color: #000000; outline: none; } \/* Quiz title \/ transformation *\/ #ays-quiz-container-74 .ays-fs-title{ text-transform: uppercase; text-align: center; text-shadow: none; } #ays-quiz-container-74 .ays-quiz-password-message-box, #ays-quiz-container-74 .ays-quiz-question-note-message-box, #ays-quiz-container-74 .ays_quiz_question, #ays-quiz-container-74 .ays_quiz_question *:not([class^='enlighter']) { color: #000000; } #ays-quiz-container-74 textarea, #ays-quiz-container-74 input::first-letter, #ays-quiz-container-74 select::first-letter, #ays-quiz-container-74 option::first-letter { color: initial !important; } #ays-quiz-container-74 p::first-letter:not(.ays_no_questions_message) { color: #000000 !important; background-color: transparent !important; font-size: inherit !important; font-weight: inherit !important; float: none !important; line-height: inherit !important; margin: 0 !important; padding: 0 !important; } #ays-quiz-container-74 .select2-container, #ays-quiz-container-74 .ays-field * { font-size: 16px !important; } #ays-quiz-container-74 .ays-fs-subtitle p { text-align: center ; } #ays-quiz-container-74 .ays_quiz_question p { font-size: 17px; text-align: center; } #ays-quiz-container-74 .ays_quiz_question { text-align: center ; margin-bottom: 10px; } #ays-quiz-container-74 .ays_quiz_question pre { max-width: 100%; white-space: break-spaces; } div#ays-quiz-container-74 .ays-questions-container .ays-field, div#ays-quiz-container-74 .ays-questions-container .ays-field input~label[for^='ays-answer-'], div#ays-quiz-container-74 .ays-questions-container .ays-modern-dark-question *, div#ays-quiz-container-74 .ays-questions-container .ays_quiz_question, div#ays-quiz-container-74 .ays-questions-container .ays_quiz_question *{ word-break: break-word; } #ays-quiz-container-74 .ays-quiz-timer p { font-size: 16px; } #ays-quiz-container-74 section.ays_quiz_redirection_timer_container hr, #ays-quiz-container-74 section.ays_quiz_timer_container hr { margin: 0; } #ays-quiz-container-74 section.ays_quiz_timer_container.ays_quiz_timer_red_warning .ays-quiz-timer { color: red; } #ays-quiz-container-74 .ays_thank_you_fs p { text-align: center; } #ays-quiz-container-74 .information_form input[type='text'], #ays-quiz-container-74 .information_form input[type='url'], #ays-quiz-container-74 .information_form input[type='number'], #ays-quiz-container-74 .information_form input[type='email'], #ays-quiz-container-74 .information_form input[type='tel'], #ays-quiz-container-74 .information_form textarea, #ays-quiz-container-74 .information_form select, #ays-quiz-container-74 .information_form option { color: initial !important; outline: none; margin-left: 0; background-image: unset; } #ays-quiz-container-74 .information_form input[type='checkbox'] { margin: 0 10px; outline: initial; -webkit-appearance: auto; -moz-appearance: auto; position: initial; width: initial; height: initial; border: initial; background: initial; } #ays-quiz-container-74 .information_form input[type='checkbox']::after { content: none; } #ays-quiz-container-74 .wrong_answer_text{ color:#ff4d4d; } #ays-quiz-container-74 .right_answer_text{ color:#33cc33; } #ays-quiz-container-74 .ays_cb_and_a, #ays-quiz-container-74 .ays_cb_and_a * { color: rgb(0,0,0); text-align: center; } #ays-quiz-container-74 iframe { \/*min-height: 350px;*\/ } #ays-quiz-container-74 label.ays_for_checkbox, #ays-quiz-container-74 span.ays_checkbox_for_span { color: initial !important; display: block; } \/* Quiz textarea height *\/ #ays-quiz-container-74 textarea { height: 100px; min-height: 100px; } \/* Quiz rate and passed users count *\/ #ays-quiz-container-74 .ays_quizn_ancnoxneri_qanak, #ays-quiz-container-74 .ays_quiz_rete_avg{ color:#f2f2f2; background-color:#000000; } #ays-quiz-container-74 .ays-questions-container > .ays_quizn_ancnoxneri_qanak { padding: 5px 20px; } #ays-quiz-container-74 div.for_quiz_rate.ui.star.rating .icon { color: rgba(0,0,0,0.35); } #ays-quiz-container-74 .ays_quiz_rete_avg div.for_quiz_rate_avg.ui.star.rating .icon { color: rgba(242,242,242,0.5); } #ays-quiz-container-74 .ays_quiz_rete .ays-quiz-rate-link-box .ays-quiz-rate-link { color: #000000; } \/* Loaders *\/ #ays-quiz-container-74 div.lds-spinner, #ays-quiz-container-74 div.lds-spinner2 { color: #000000; } #ays-quiz-container-74 div.lds-spinner div:after, #ays-quiz-container-74 div.lds-spinner2 div:after { background-color: #000000; } #ays-quiz-container-74 .lds-circle, #ays-quiz-container-74 .lds-facebook div, #ays-quiz-container-74 .lds-ellipsis div{ background: #000000; } #ays-quiz-container-74 .lds-ripple div{ border-color: #000000; } #ays-quiz-container-74 .lds-dual-ring::after, #ays-quiz-container-74 .lds-hourglass::after{ border-color: #000000 transparent #000000 transparent; } \/* Stars *\/ #ays-quiz-container-74 .ui.rating .icon, #ays-quiz-container-74 .ui.rating .icon:before { font-family: Rating !important; } \/* Progress bars *\/ #ays-quiz-container-74 #ays_finish_quiz_74 .ays-progress { border-color: rgba(0,0,0,0.8); } #ays-quiz-container-74 #ays_finish_quiz_74 .ays-progress-bg { background-color: rgba(0,0,0,0.3); } #ays-quiz-container-74 . { background-color: #2fa0ca; } #ays-quiz-container-74 . { background-color: #000000; } #ays-quiz-container-74 .ays-progress-value { color: #000000; text-align: center; } #ays-quiz-container-74 .ays-progress-bar { background-color: #2fa0ca; } #ays-quiz-container-74 .ays-question-counter .ays-live-bar-wrap { direction:ltr !important; } #ays-quiz-container-74 .ays-live-bar-fill{ color: #000000; border-bottom: 2px solid rgba(0,0,0,0.8); text-shadow: 0px 0px 5px #f2f2f2; } #ays-quiz-container-74 .ays-live-bar-fill.ays-live-fourth, #ays-quiz-container-74 .ays-live-bar-fill.ays-live-third, #ays-quiz-container-74 .ays-live-bar-fill.ays-live-second { text-shadow: unset; } 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This place is where you will find the important MCQs of Differentiation.&hellip;<\/p>\n","protected":false},"author":2,"featured_media":245,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[8,9,7],"class_list":["post-244","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math","tag-ecat-mcqs","tag-entry-test-preparation","tag-math-mcqs","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>2nd Year Math Chapter 2 Differentiation MCQs With Answers<\/title>\n<meta name=\"description\" content=\"Get the important 2nd Year Math Chapter 2 Differentiation MCQs With Answers here. 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