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

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1. At what rate in cm² per cm is the area of the circle changing w.r.t its radius when the radius is 5cm?

10πcm²/cm

5πcm²/cm

3πcm²/cm

20πcm²/cm

2. Differentiate the function w.r.t x: y= 5(x+5)

25x²

25

5

5x

3. Differentiate the function wrt x: (2x-7)²

x²-14

x+7x

8x-28

28x²

4. The displacement xcm from a fixed point of a particle moving in a straight line after time t (s) is given by

x = 12t - 15t² + 4t³.

Find its acceleration in m/s², after 3s.

72 m/s2

12 m/s2

36 m/s2

42 m/s2

5. Find the minimum value of the function 2x³ - 6x²

8

5

-5

-8

6. Find the gradient of the curve y = 2√x - 1/x at the point x = 1

2

0

1

3

7. Differentiate w.r.t x 7x^{4 }- 5x

14x

28x³-5

28+5x²

28x² -5x

8. Find dy/dx if :

y = cos2xsinx + sin2xcosx

-3cos2x cosx + 3sin2x sinx

3cos2x cosx - 3sin2x sinx

-3cos2x cosx - 3sin2x sinx

3sin2x sinx

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

find dA/dV

r/2

r/3

2/r

3/r

10. 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

10π cm/s

8π cm/s

4π cm/s

11. A curve has equation y = x³ -4x² - 3x + 18, the point P(-2, 0) lies on the curve. Find the gradient of the tangent to the curve at P.

25

29

21

22

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

3x²(4x+5)(2x+5)²

10x(2x+5)²

4x+5

2x+20

13. Differentiate the function wrt x: y = x³(x²-3x+1)

x²(5x²-12x+3)

x+12

x²(x+3)

5x

14. Differentiate, with the respect to x:

cosx - x sinx

-2sinx - xcosx

-2sinx + xcosx

xcosx

2sinx -xcosx

15. Differentiate w.r.t x

cos³x

-3cos²x

3sinx

3cos²xsinx

-3cos²xsinx

16. If y = x³ + 3x²,

find 2dy/dx - x d²y/dx²

6x²

6x

4

6

17. The distance S (m) covered in time t (s) by a body is

s = 5(1 -e^{-4t}). Find its speed, in m/s, when t = 0

10

30

14

20

18. Find the derivative of h(x) =

3-2x-¹

3x-2

8x-8x-¹

4x-¹

19. The radius r of a circular disc is increasing at the rate of 0.5 cm/s. At what rate is the area of the disc increasing when its radius is 6 cm?

36π cm²/s

6π cm²/s

18π cm²/s

3π cm²/s

20. Find the differential coefficient of

y = -5/(x²+4) at the point (1, -1)

5/2

-2/5

2/5

-5/2

21. Differentiate w.r.t x 3x²+4x

6x+4x

6x

6x+4

3x+4

22. Determine the turning point of the curve

y = x² + 250/x

(-5, 35)

(-2, 7)

(2, 7)

(5, 35)

23. Find the derivative of y = sin²(5x) wrt x

xsin²5x

10sin5xcos5x

sin5xcos5x

xcos²5x

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

1 /(cosx -1)

-1 /(1- cosx)

x

cos x

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