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

A) x ∈ [1, ∞), y ∈ [0, ∞)

B) x < 0, y < 0

C) x ∈ R, y ∈ R

D) x ∈ [1, ∞), y ∈ (0, ∞]

2 / 20

2. d/dx (ax + b)ⁿ =

A) n(a^n−1x + b)

B) n(a^n−1x)

C) n(a^x + b)^ n−1

D) na(ax + b) ^n−1

3 / 20

3. limx→a f(x)−f(a)/x−a =

A) f(0)

B) f′(x)

C) f′(a)

D) f(x − a)

4 / 20

4. d/dx (Sina) =

A) a cos a

B) 0

C) cos a

D) – a cos a

5 / 20

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

A) x > 0, y > 0

B) x ∈[ − 1,1], y ∈ R

C) x ∈ R, y ∈ R

D) x ∈ [−1,1], y ∈ R − {0}

6 / 20

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

A) x < 0, y < 0

B) x > 0, y > 0

C) x ∈ R, y > 0

D) x ∈ R, x > 0

7 / 20

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

A) imaginary number

B) real number

C) Irrational number

D) rational number

8 / 20

8. The notation ḟ(x) is used by

A) Leibnitz

B) Newton

C) Cauchy

D) Lagrange

9 / 20

9. If y = e−ax , then y2 =

A) – a^2 e^ax

B) – ae^ax

C) a^2 e^−2ax

D) – a^2 e^−2ax

10 / 20

10. d/dx 2^x =

A) ln2/2^x

B) 2^x

C) 2^x ln2

D) 2^x ln2

11 / 20

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

A) None of these

B) +iv only

C) +iv or –iv

D) –iv only

12 / 20

12. d/dx tan3x =

A) 1/3 sec^2 3x

B) sec^2 x

C) cot3x

D) 3 sec2 3x

13 / 20

13. d/dx(xⁿ) = nxⁿ⁻¹ is called

A) Quotient rule

B) Constant rule

C) Power rule

D) Product rule

14 / 20

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

A) x ∈ R, y ∈ R

B) x ∈[− 1,1], y ∈ R

C) x > 0, y >0

D) x ∈ R[−1,1], y ∈ R

15 / 20

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

A) Newton

B) Leibnitz

C) Lagrange

D) Cauchy

16 / 20

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

A) f(x)g′(x) − g(x)f′(x)

B) f(x)g′(x) + g(x)f′(x)

C) f′ (x) + g′ (x)

D) f′(x) − g′(x)

17 / 20

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

A) Negative

B) Undefined

C) Zero

D) Positive

18 / 20

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

A) 2e^2x

B) e^2x

C) 4 e^2x

D) 16 e^2x

19 / 20

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

A) Negative

B) Positive

C) Undefined

D) Zero

20 / 20

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

A) x ∈[ − 1,1], y ∈ R

B) x ∈ (0,1], y ∈ [0, ∞)

C) x ∈ [−1,1], y ∈ R − {0}

D) x ∈ R, y ∈ R

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2nd Year Math Chapter 2 Differentiation MCQs With Answers

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