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

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1. Differentiate w.r.t θ

( sin θ / 3+ 2cos θ )

3cos θ + 2/(3 + 2cos θ )²

3cos θ + 2

3cos θ + 2/(3 + 2cos θ)

1/(3 + 2cos θ )²

2. 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.

4m/s

8m/s

16m/s

10m/s

3. If y = x² - 1/x, find dy/dx

2 - x²

2x + 1/x²

3x

1/2x²

4. 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

21

22

29

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

-1

0

2

1

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

8x²

6x

x²-3

8x

7. Differentiate w.r.t x 3x²+4x

3x+4

6x+4

6x

6x+4x

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

(1, 3)

(5, 7)

(3, 4)

(2, 9)

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

28x²

8x-28

x+7x

x²-14

10. Find the derivative of f(x)=6x³ − 9x + 4x

18x²-9

x²+3

18-x

x²-9

11. Find the minimum value of the function

y = x³ + 3x² - 9x + 1

-4

-2

-3

-1

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

4π cm³/s

6π cm³/s

8π cm³/s

2π cm³/s

13. Differentiate w.r.t x

sin³x

3sin²xcosx

-3sin²xcosx

-3cos²xsinx

3sin²x

14. Find the differential coefficient of

y = -5/(x²+4) at the point (1, -1)

2/5

-2/5

-5/2

5/2

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

sin5xcos5x

xsin²5x

10sin5xcos5x

xcos²5x

16. If y = 8x² - 5x, find the approximate change in y if x changes from 1 to 1.05.

1.0

1.5

0.25

0.55

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

-8

8

-5

5

18. Differentiate (x² - 1/x)² wrt x

4x³ -2/x³ -2

2x²-2

2/x³ +3x +2

x³-3x²+2

19. 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?

4 cm²

3cm²

2cm²

1cm²

20. If x³ + y³+ 6xy = 0,

find dy/dx by implicit differentiation

(2y + x²)/ (2x + y²)

- (2y + x²)/(2x + y²)

- (2y + x²)/ y

x/(2x + y²)

21. Find the maximum and minimum values of the

function 3x² - x³

max = 1, min = -1

max = 4, min = 0

max = 10, min = 4

max =-2, min = -6

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

5 + 2/x²

5 + 2/x

2/ x3

5 + 2/x³

23. An object dropped from rest has position s = 7t² metres below its starting point. At what time does the object have velocity of 35 m/s.