Elective Mathematics

Question 1

1If y = 4x², then dy/dx = ___x¹

Easy

Your answer (fill in the blank)

Question 2

2Differentiate y = x³ sin x.

Hard

A. x³ cos x − 3x² sin x B. 3x² cos x C. x³ cos x + 3x² sin x D. x³ cos x

Question 3

3Differentiate y = ln(4x).

Hard

A. ln 4 B. 1/x C. 1/(4x) D. 4/x

Question 4

4d/dx(x⁵) = 5x⁴.

Easy

A. True B. False

Question 5

5Differentiate y = e^(6x).

Medium

A. 6e^(6x) B. e^(6x) C. e^(6) D. 6x e^(5x)

Question 6

6d/dx(sin 2x) = cos 2x.

Medium

A. True B. False

Question 7

7If y = 6x⁴, then dy/dx = ___x³

Easy

Your answer (fill in the blank)

Question 8

8Find dy/dx at x = 1 for y = 6x⁴ + 5x.

Medium

A. 35 B. 30 C. 11 D. 29

Question 9

9Differentiate y = 4x² + 4x.

Easy

A. 8x¹ + 4 B. 4x¹ + 4 C. 8x² + 4 D. 8x¹

Question 10

10The product rule is d(uv)/dx =

Easy

A. u dv/dx − v du/dx B. du/dx × dv/dx C. u dv/dx + v du/dx D. u/v