2nd Year Math Chapter 2 Differentiation MCQs With Answers

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.

2nd Year Math Chapter 2 Differentiation MCQs With Answers

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2nd Year Math Chapter 2

1 / 20

1. y = tanh⁻¹x if and only if x = tanhy is valid when

A) x > 0, y >0

B) x ∈ R[−1,1], y ∈ R

C) x ∈ R, y ∈ R

D) x ∈[− 1,1], y ∈ R

2 / 20

2. d/dx tan3x =

A) 1/3 sec^2 3x

B) 3 sec2 3x

C) cot3x

D) sec^2 x

3 / 20

3. y = cosh⁻¹x if and only if x = coshy is valid when

A) x < 0, y < 0

B) x ∈ [1, ∞), y ∈ (0, ∞]

C) x ∈ R, y ∈ R

D) x ∈ [1, ∞), y ∈ [0, ∞)

4 / 20

4. The notation dy/dx or df/dx is used by

A) Lagrange

B) Leibnitz

C) Newton

D) Cauchy

5 / 20

5. The notation ḟ(x) is used by

A) Newton

B) Leibnitz

C) Cauchy

D) Lagrange

6 / 20

6. y = coth⁻¹x if and only if x = cothy is valid when

A) x ∈ R, y ∈ R

B) x > 0, y > 0

C) x ∈[ − 1,1], y ∈ R

D) x ∈ [−1,1], y ∈ R − {0}

7 / 20

7. d/dx (ax + b)ⁿ =

A) n(a^n−1x + b)

B) na(ax + b) ^n−1

C) n(a^n−1x)

D) n(a^x + b)^ n−1

8 / 20

8. d/dx (Sina) =

A) – a cos a

B) cos a

C) a cos a

D) 0

9 / 20

9. If y = e^2x, then y2=

A) 2e^2x

B) 4 e^2x

C) 16 e^2x

D) e^2x

10 / 20

10. If a function f is increasing within [a, b] ,then slope of tangent to its graph within [a, b] remains

A) Zero

B) Undefined

C) Negative

D) Positive

11 / 20

11. d/dx(xⁿ) = nxⁿ⁻¹ is called

A) Product rule

B) Quotient rule

C) Power rule

D) Constant rule

12 / 20

12. y = sinh⁻¹x if and only if x = sinhy is valid when

A) x > 0, y > 0

B) x ∈ R, x > 0

C) x < 0, y < 0

D) x ∈ R, y > 0

13 / 20

13. If y = e−ax , then y2 =

A) a^2 e^−2ax

B) – a^2 e^−2ax

C) – a^2 e^ax

D) – ae^ax

14 / 20

14. d/dx 2^x =

A) ln2/2^x

B) 2^x

C) 2^x ln2

D) 2^x ln2

15 / 20

15. limx→a f(x)−f(a)/x−a =

A) f′(x)

B) f′(a)

C) f(x − a)

D) f(0)

16 / 20

16. d/dx [f(x) + g(x)] =

A) f′(x) − g′(x)

B) f(x)g′(x) + g(x)f′(x)

C) f(x)g′(x) − g(x)f′(x)

D) f′ (x) + g′ (x)

17 / 20

17. y = sech⁻¹x if and only if x = sechy is valid when

A) x ∈[ − 1,1], y ∈ R

B) x ∈ [−1,1], y ∈ R − {0}

C) x ∈ R, y ∈ R

D) x ∈ (0,1], y ∈ [0, ∞)

18 / 20

18. The change in variable x is called the increment of x. It is denoted by δx which is

A) +iv or –iv

B) +iv only

C) –iv only

D) None of these

19 / 20

19. If a function f is increasing within [a, b] ,then slope of tangent to its graph within [a, b] remains

A) Zero

B) Undefined

C) Negative

D) Positive

20 / 20

20. d/dx (ax + b)ⁿ = na(ax + b)ⁿ⁻¹ is valid only when n must be:

A) rational number

B) imaginary number

C) Irrational number

D) real number

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2nd Year Math Chapter 2 Differentiation MCQs With Answers

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