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Unit 3: Differentiability of function - Practice Quiz

MTH110 — Remedial Mathematics 60 Questions
0 Correct 0 Wrong 60 Left
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1 The derivative of by first principle is defined as which of the following?

derivatives by first principle Easy
A.
B.
C.
D.

2 Using first principle, the derivative of is:

derivatives by first principle Easy
A.
B.
C.
D.

3 According to the product rule, equals:

algebra of derivative of functions Easy
A.
B.
C.
D.

4 The quotient rule for is:

algebra of derivative of functions Easy
A.
B.
C.
D.

5 The derivative of a constant function is:

algebra of derivative of functions Easy
A.
B.
C.
D.

6 If a function is differentiable at a point, then at that point it is necessarily:

differentiability Easy
A. Discontinuous
B. Undefined
C. Continuous
D. Constant

7 The function is not differentiable at which point?

differentiability Easy
A.
B.
C.
D.

8 The derivative of is:

derivatives of composite functions Easy
A.
B.
C.
D.

9 If , then according to the chain rule equals:

chain rule Easy
A.
B.
C.
D.

10 The derivative of with respect to is:

chain rule Easy
A.
B.
C.
D.

11 For the equation , differentiating implicitly gives :

derivatives of implicit functions Easy
A.
B.
C.
D.

12 In implicit differentiation of a function of and , the derivative of with respect to is:

derivatives of implicit functions Easy
A.
B.
C.
D.

13 The derivative of with respect to is:

derivatives of inverse trigonometric functions Easy
A.
B.
C.
D.

14 The derivative of with respect to is:

derivatives of inverse trigonometric functions Easy
A.
B.
C.
D.

15 The derivative of with respect to is:

derivatives of exponential and logarithmic functions Easy
A.
B.
C.
D.

16 The derivative of (natural log) with respect to is:

derivatives of exponential and logarithmic functions Easy
A.
B.
C.
D.

17 Logarithmic differentiation is most useful for differentiating functions of the form:

logarithmic differentiation Easy
A.
B.
C.
D.

18 If and , then equals:

derivatives of functions in parametric forms Easy
A.
B.
C.
D.

19 The second order derivative of with respect to is written as:

second order derivatives Easy
A.
B.
C.
D.

20 If , then the second order derivative is:

second order derivatives Easy
A.
B.
C.
D.

21 Using the first principle, the derivative of is:

derivatives by first principle Medium
A.
B.
C.
D.

22 Using the first principle, the derivative of is:

derivatives by first principle Medium
A.
B.
C.
D.

23 If , then equals:

algebra of derivative of functions Medium
A.
B.
C.
D.

24 If , then is:

algebra of derivative of functions Medium
A.
B.
C.
D.

25 The function is:

differentiability Medium
A. Neither continuous nor differentiable at
B. Continuous everywhere but not differentiable at
C. Differentiable everywhere
D. Differentiable only at

26 For what value of is differentiable at ?

differentiability Medium
A.
B.
C.
D.

27 If , then is:

derivatives of composite functions Medium
A.
B.
C.
D.

28 The derivative of with respect to is:

derivatives of composite functions Medium
A.
B.
C.
D.

29 If , then equals:

chain rule Medium
A.
B.
C.
D.

30 If , then is:

chain rule Medium
A.
B.
C.
D.

31 If , then is:

derivatives of implicit functions Medium
A.
B.
C.
D.

32 If , then equals:

derivatives of implicit functions Medium
A.
B.
C.
D.

33 The derivative of with respect to is:

derivatives of inverse trigonometric functions Medium
A.
B.
C.
D.

34 If , then is:

derivatives of inverse trigonometric functions Medium
A.
B.
C.
D.

35 The derivative of is:

derivatives of exponential and logarithmic functions Medium
A.
B.
C.
D.

36 If , then equals:

derivatives of exponential and logarithmic functions Medium
A.
B.
C.
D.

37 If , then is:

logarithmic differentiation Medium
A.
B.
C.
D.

38 If , then equals:

logarithmic differentiation Medium
A.
B.
C.
D.

39 If and , then is:

derivatives of functions in parametric forms Medium
A.
B.
C.
D.

40 If , then is:

second order derivatives Medium
A.
B.
C.
D.

41 Using the first principle, the derivative of is:

derivatives by first principle Hard
A.
B.
C.
D.

42 By first principle, equals:

derivatives by first principle Hard
A.
B.
C.
D.

43 The number of points in where is NOT differentiable is:

differentiability Hard
A.
B.
C.
D.

44 Let for and . Which statement is true?

differentiability Hard
A. and is differentiable everywhere
B. does not exist
C. is continuous but nowhere differentiable
D.

45 If , then equals:

algebra of derivative of functions Hard
A.
B.
C.
D.

46 If , then is:

derivatives of composite functions Hard
A.
B.
C.
D.

47 If , then equals:

chain rule Hard
A.
B.
C.
D.

48 If , then equals:

derivatives of implicit functions Hard
A.
B.
C.
D.

49 If , then equals:

derivatives of implicit functions Hard
A.
B.
C.
D.

50 If , then equals:

derivatives of inverse trigonometric functions Hard
A.
B.
C.
D.

51 If for , then equals:

derivatives of inverse trigonometric functions Hard
A.
B.
C.
D.

52 The derivative of is:

derivatives of exponential and logarithmic functions Hard
A.
B.
C.
D.

53 If , then equals:

logarithmic differentiation Hard
A.
B.
C.
D.

54 If , then equals:

logarithmic differentiation Hard
A.
B.
C.
D.

55 For the cycloid , , equals:

derivatives of functions in parametric forms Hard
A. with opposite sign
B.
C.
D.

56 If and , then equals:

derivatives of functions in parametric forms Hard
A.
B.
C.
D.

57 If , then equals:

second order derivatives Hard
A.
B.
C.
D.

58 If , which relation holds?

second order derivatives Hard
A.
B.
C.
D.

59 If and , then equals:

derivatives of functions in parametric forms Hard
A.
B.
C.
D.

60 If for , then equals:

derivatives of inverse trigonometric functions Hard
A.
B.
C.
D.
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