Welcome to your Differentiation(Senior Class Math Study by Topics)

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1. Find, with respect to x, the derivative of sin x /(1- cos x)

-1 /(1- cosx)

x

cos x

1 /(cosx -1)

2. d/dx cos(3x² - 2x) is equal to

-6x+2cosx

sin(3x²

sin(3x² - 2x)

-(6x-2)sin(3x² - 2x)

3. Given that V = 4/3 πr³ and A = 4πr²,

find dA/dV

3/r

r/2

2/r

r/3

4. Differentiate w.r.t x

sin³x

3sin²xcosx

-3cos²xsinx

3sin²x

-3sin²xcosx

5. Using the product rule differentiate wrt x (x²+3)(2x-1)

6x²-2x+6

6x+ 2

2x²

x²+3x-1

6. Find the maximum value of the function 3x²-x³

-2

4

-3

1/2

7. A rectangular goat pen is to be fenced off near the brick wall. The total length of the fence is 20m. What must be the length of the side parallel to the brick wall to yield the greatest area?

10 m

8 m

12 m

16m

8. If the radius of the base of a cone is decreasing at 2 cm/s, find the rate of increase in volume when the radius of the base is 5 cm.

50π cm³/s

20.5π cm³/s

25π cm³/s

10π cm³/s

9. Find dy/dx

if y = log_{e}tan2x

2sec²2x

2cot²xsecx

2cot2x

2cot2xsec²2x

10. Find the derivative of (2+3x)(1-x) with respect to x

11. The distance s metres after time t second covered by a particle moving along a straight line is given by

s = t³ - t² - t - 2

Find the average acceleration between t = 2 and t = 4

3ms-²

4ms-²

6ms-²

2ms-²

12. A ball is thrown vertically upwards and its height s metres after t seconds is given by s = 16t - 4t². Find the time when the velocity is 8 m/s.

2s

4s

1s

3s

13. If x³ + y³+ 6xy = 0,

find dy/dx by implicit differentiation

- (2y + x²)/ y

- (2y + x²)/(2x + y²)

(2y + x²)/ (2x + y²)

x/(2x + y²)

14. Differentiate w.r.t θ

( sin θ / 3+ 2cos θ )

3cos θ + 2

3cos θ + 2/(3 + 2cos θ)

3cos θ + 2/(3 + 2cos θ )²

1/(3 + 2cos θ )²

15. Differentiate 5x - 1/x² from the first principle

2/ x3

5 + 2/x²

5 + 2/x³

5 + 2/x

16. The side of a square of length 5 cm is increasing at 0.1m/s. What is the rate of increase of the area of the square?

1cm²

3cm²

2cm²

4 cm²

17. Find, w.r.t.x, the derivative of

4(x - 3/x)³

4(1+3/x²)

4(x - 3/x)³(1+3/x²)

(1+3/x²)

18. Find, from the first principles, the derivative, with respect to x of 2x² + 1/x

4x - 1/x²

4x - 1/x

4x

1/x²

19. Differentiate the functions wrt x: (x-2)(3x+5)

6x-1

3x²

3x+2

4x+4

20. Find dy/dx if :

y = cos2xsinx + sin2xcosx

3sin2x sinx

3cos2x cosx - 3sin2x sinx

-3cos2x cosx - 3sin2x sinx

-3cos2x cosx + 3sin2x sinx

21. If y = 2xcos2x - sin2x, find dy/dx when x = π/4

π

π/4

π/2

-π

22. Differentiate the function wrt x:

1/2 - 1/4x²

3x + 1/4x²

1/2 + 3x + 1/4x²

1/4x²

23. Use the product rule to differentiate wrt x x³(2x+5)³

4x+5

10x(2x+5)²

2x+20

3x²(4x+5)(2x+5)²

24. If

find dy/dx

1/(x+1)³

(x-1)³

1/(x-1)³

(x+1)³

25. Differentiate the function w.r.t x: y = 4(x² - 3)