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

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1. Find the differential coefficient of

at the point (1, -1)

3

1/3

2/5

5/2

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

0

2

1

-1

3. Differentiate the function wrt x:

2(x - 1/x²)

x²+2

2-3x²

1/x²

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

(6x²+3)cos(2x³ + 3x - 4)

sin4x+x

cos(2x³ + 3x - 4)

6xsin(2x³ + 3x - 4)

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

π/4

π/2

π

-π

6. The distance s metres travelled by a particle in time t seconds is given by s = 12 + 40t - 2t². Find the distance travelled by the particle before coming to rest.

200m

180m

120m

212m

7. If y = x³ + 3x²,

find 2(dy/dy) - x(d²y/dx²)

4x

6x

5x

2x

8. Differentiate w.r.t θ

( sin θ / 3+ 2cos θ )

3cos θ + 2

3cos θ + 2/(3 + 2cos θ )²

3cos θ + 2/(3 + 2cos θ)

1/(3 + 2cos θ )²

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

10x(2x+5)²

2x+20

3x²(4x+5)(2x+5)²

4x+5

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

10sin5xcos5x

xsin²5x

xcos²5x

sin5xcos5x

11. If x³ + y³+ 6xy = 0,

find dy/dx by implicit differentiation

x/(2x + y²)

- (2y + x²)/ y

- (2y + x²)/(2x + y²)

(2y + x²)/ (2x + y²)

12. Differentiate w.r.t x: x-4x³

1-4x

1-4x²

1-12x²

4x

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

find dA/dV

r/2

2/r

r/3

3/r

14. Find dy/dx if :

y = cos2xsinx + sin2xcosx

3sin2x sinx

-3cos2x cosx + 3sin2x sinx

3cos2x cosx - 3sin2x sinx

-3cos2x cosx - 3sin2x sinx

15. A particle moves along a straight line from a fixed point O such that its distance s metres at time t seconds is given by s = 2 +8t - 0.5t². Find the velocity of the particle as it passes point O.

8m/s

4m/s

10m/s

16m/s

16. If

find dy/dx

1/(x-1)³

1/(x+1)³

(x-1)³

(x+1)³

17. 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

6ms-²

2ms-²

4ms-²

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

6x

8x

8x²

x²-3

19. Use chain rule to differentiate (3x+4)³

3x²

9(3x + 4)²

12x³

3x² + 4

20. 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.

3s

2s

1s

4s

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

5 + 2/x²

2/ x3

5 + 2/x³

5 + 2/x

22. Find the point (x, y) on the Euclidean plane where the curve y = 2x² -2x + 3 has 2 as gradient

(5, 7)

(1, 3)

(2, 9)

(3, 4)

23. Find, w.r.t.x,

the derivative of (2x² - x + 3)³

3(4x-1)(2x² - x + 3)³

2(2x+3)

3(4x-1)

7(2x² - x + 3)³

24. If 3x² - 5y² - 1 = 0,

find the value of dy/dx at point (5, -2)

2

-1

-3

3

25. 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.