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

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1. Differentiate sinx - xcosx

xcosx

sinx + cosx

xsinx

cosx + xsinx

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

find dA/dV

r/3

r/2

2/r

3/r

3. Find dy/dx

if y = log_{e}tan2x

2cot2x

2sec²2x

2cot2xsec²2x

2cot²xsecx

4. Differentiate w.r.t x

sin³x

-3cos²xsinx

3sin²x

3sin²xcosx

-3sin²xcosx

5. Find the derivative of f(y) =

y-2

4y

2-2yy³

2y-4y-³

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

π

π/4

-π

π/2

7. What is the rate of change of the volume v of a hemisphere with respect to its radius r when r = 2?

6π cm³/s

4π cm³/s

8π cm³/s

2π cm³/s

8. From the curve y =(4 - x)(3 + x), find the gradients of the curve at the points P(-1, 10) and Q(3, 6)

mp = 3, mq = -6

mp = -3, mq = 4

mp = -4, mq = 4

mp = 3, mq = -5

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

4x+5

10x(2x+5)²

3x²(4x+5)(2x+5)²

2x+20

10. Find, from the first principles, the derivative with respect to x of the function

y = 2x² - x + 3

4x

4x - 2

4x - 4

4x - 1

11. Differentiate the function wrt x (x+3)³

x²+3

x²+9

x+3x²

3(x+3)²

12. A body moves along x-axis and its position is given by x = 4.5t³ - 9t² -4t where x is in metres and t is in seconds. Find the velocity and acceleration at t = 2 s.

14 m/s and 18 m/s²

14 m/s and 36 m/s²

18 m/s and 14 m/s²

36 m/s and 14 m/s²

13. 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?

3cm²

1cm²

2cm²

4 cm²

14. If y = 3cos4x, find dy/dx

-12sin4x

12cos4x

12sin4x

-12cos4x

15. 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?

8 m

16m

12 m

10 m

16. Determine the turning point of the curve

y = x² + 250/x

(2, 7)

(-5, 35)

(-2, 7)

(5, 35)

17. Find the minimum value of the function 3x²-x³

2

1

0

-1

18. Differentiate wrt x: x³(x - 1)

3x+2

x³ + 3x²(x-1)

(x²+2)x

1+x²

19. Differentiate w.r.t x 5x³

5x²

15x

5x

15x²

20. The radius of a circle s increasing at the rate of 0.05 cm/s. Find the rate of increase of the circumference when the radius of the circle is 4 cm.

0.2π cm/s

8π cm/s

10π cm/s

4π cm/s

21. Differentiate w.r.t θ

( sin θ / 3+ 2cos θ )

3cos θ + 2

1/(3 + 2cos θ )²

3cos θ + 2/(3 + 2cos θ )²

3cos θ + 2/(3 + 2cos θ)

22. 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

1s

4s

3s

23. 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

2ms-²

6ms-²

4ms-²

24. Find the derivative of y = sin(2x³ + 3x - 4) wrt x