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

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1.

An object is thrown vertically downwards from top of a tower and after t seconds it is at a distance S m below the top, where

s = 30t + 4.9t².

Determine its velocity at the end of the first second

41.8 m/s

16 m/s

32.2 m/s

39.8 m/s

2.

The radius of a spherical balloon is increasing at the rate of 0.25cm/s, find the rate at which the volume is increasing when its radius is 4cm

4π cm³/s

7π cm³/s

12π cm³/s

16π cm³/s

3.

Find the derivative of h(x) =

8x-8x-¹

4x-¹

3x-2

3-2x-¹

4.

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.

18 m/s and 14 m/s²

14 m/s and 36 m/s²

14 m/s and 18 m/s²

36 m/s and 14 m/s²

5.

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

8x-28

x²-14

28x²

x+7x

6.

Differentiate the function wrt x:

2(x - 1/x²)

1/x²

x²+2

2-3x²

7.

Differentiate the function wrt x: y = √x

x²

√x

2√x

1/2√x

8.

Differentiate the functions wrt x: 5(3x-4)²

60x+4x²

3x²+4

30(3x-4)

60x²

9.

Find the minimum value of the function 3x²-x³

0

2

-1

1

10.

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

20

30

14

11.

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

12.

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.

3 s

2.5 s

14 s

2 s

13.

Differentiate w.r.t x

cos³x

3cos²xsinx

-3cos²xsinx

3sinx

-3cos²x

14.

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

8π cm³/s

2π cm³/s

6π cm³/s

15.

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

6x²-2x+6

2x²

x²+3x-1

6x+ 2

16.

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.

4s

3s

1s

2s

17.

Differentiate the function wrt x: y = x(x³+7)

x³+7

2x+7

x²+7

x³

18.

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

3πcm²/cm

10πcm²/cm

20πcm²/cm

5πcm²/cm

19.

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

-8

5

8

-5

20.

Differentiate w.r.t x 5x³

15x²

15x

5x

5x²

21.

Find the values of x at the turning points of the curve

y = 2x³ - 3x² - 12x + 8

1 or 3

-1 or 2

2 or 3

3 or 4

22.

A curve has equation y = x³ -4x² - 3x + 18, find dy/dx

x²-3x

8x+18

3x²-8x-3

x² +12

23.

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

8x²

8x

x²-3

6x

24.

If 3x² - 5y² - 1 = 0,

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

2

3

-3

-1

25.

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?