Free Printable Differentiation - Sum, Diff, Chain Rules and First Principle

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Differentiation - Sum, Diff, Chain Rules and First Principle

Total questions: 60

Worksheet time: 2hrs 26mins

Name

Class

Date

Differentiate sin³x

3sin²x

3sin²xcosx

cos³x

3sinxcosx

Differentiate sinx³

3x²cosx³

3x²sinx³

sin3x²

3x²sinx³cosx³

Differentiate cos(1-3x)

-sin(1-3x)

-3cos(1-3x)

3sin(1-3x)

-3cos(1-3x)sin(1-3x)

Differentiate sin(2x-2)

2cos(2x-2)

cos(2x-2)

2sin(2x-2)cos(2x-2)

2sin(2x-2)

Differentiate cos(x²+x)

(-2x-1)sin(x²+x)

-sin(x²+x)

(-2x+1)sin(x²+x)

-sin(x²+x)cos(x²+x)

Differentiate ln(sinx)

secx

cosecx

cotx

Differentiate ln(cos²x)

2secx

sec²x

-2tanx

½cosec²x

Differentiate ln(cos3x)

3sec3x

tan3x

sec3x

-3tan3x

Differentiate sin³xcosx

3sin²xcosx+sin⁴x

3sin²xcosx-sin⁴x

3cos²xsin²x-sin⁴x

3cos²xsin²x+sin⁴x

10.

-2x² - x + 9

-2x² + x + 9

2x² - x + 9

2x² - x - 9

11.

Find the derivative of the function:

f (x) = 2x - 5x⁶

f '(x)= 2 - 30x

f '(x) = 2-30x⁵

f '(x) = -30x⁵

f '(x) = -150x⁴

12.

Set up the derivative of y=(3x⁴- 7)*(5x²+ 1)

(12x³)*(10x)

(3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

(3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

13.

Find the derivative of y = 2x² (3x - 4)

6x³ - 8x²

18x² - 16x

15x²- 6x

6x - 4

14.

Find theDerivative

x⁵-3

-10x⁶

x⁵-5

-10x^-6

15.

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

x³ + x²- x

4x³ + 12x²+ 4x

4x + 12x - 4x

4x³ + 12x²- 4x

16.

Find the derivative

9x²+2

3(x²+2)/(x²+2)²

(-3x²+4x +6)/(x²+2)²

(-3x²+10)/(x²+2)²

17.

Find the derivative of the function of time t: y = 6t + 15t²- 2

What is the velocity of the function at time t = 2 s?

64 m/s

60 m/s

66 m/s

70 m/s

18.

The position of an object is given by y = 2t + 3t³. what is the velocity of the object at t = 2 s?

38 m/s

27 m/s

16 m/s

49 m/s

19.

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?

v = 0

v = 1

v = -1

v = -2

20.

Find the derivative.

f(x) = -8x^-3 + 5x - x²

f'(x) = -24x^-4 + 5 - 2x

f'(x) = 24x^-4 + 5 - 2x

f'(x) = 24x^-2 + 5 - 2x

f'(x) = 24x^-4 + 5 - 2x

21.

Find the derivative
f(t) = (t² + 2t)⁵

f'(t) = 5(2t+2)⁴

f'(t) = 5(t² + 2t)⁴

f'(t) = 5(t² + 2t)⁴(2t)

f'(t) = 5(t² + 2t)⁴(2t + 2)

22.

16x^-1/2

-4x^-3/2

4x^1/2

-4x^-3/2

23.

5 / (2x+3)²

13 / (2x+3)²

(12x + 13) / (2x+3)²

12x+13

24.

Find the derivative of f(x) = 6x³⁰-2x¹⁵ + 4x³ - 2x + 1

f'(x) = 18x²⁹+ 30x¹⁵ + 12x³

f'(x) = 180x²⁹ - 30x¹⁴+ 12x²

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² - 2

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² +1

25.

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle?

v(t) = -2

v(t) -2t - 1

v(t) = t³

v(t) = -t

26.

f(x)=5x
find f'(x)

27.

f(x)=x³^f'(x)=

x²

3x²

28.

g(x)=7x+1
g'(x)=

7x+1

29.

y=5x²+ 3x + 9
dy/dx =

10x

10x+3

10x²+3

30.

f(x)= 9/∛x
f'(x) =

9x^-1/3

-3x^-4/3

-9x^2/3

-3x^2/3

31.

Derivative means the same thing as

slope of the tangent line

slope of the normal line

exponent

potato

32.

Select the correct derivative of:

4 cos x + 3x - x^½

3 + ½ x^-½ - 4 sin x

3 - ½ x^1.5 - 4 sin x

3 - ½ x^-½ - 4 sin x

3 - ½ x^-½ + 4 sin x

33.

Select the correct derivative of:

3e^x - 2x³ + 3

3 - 9x²

3e^x + 2x² + 3x

- 6x² + 3

3e^x - 6x²

34.

Select the correct derivative of:

- 2x² + 4e^2x + 3 ln x

8e^2x - 4x + 3

- 4x + 8e^2x + 3/x

- 4x + 8e^x + 3/x

4x + 8e^x + 3/x

35.

Select the correct value of the derivative of:

5x + 2 sin x if x = 1

6.081

6.683

5.035

36.

Select the correct value of the derivative of:

3 cos x + ln x

if x = 2

-2.035

0.7978

3.421

0.5884

37.

Select the correct derivative of:

3 sin x + 2 cos x + 5:

cos x - sin x + 5

( - 2 sin x + cos x )

5 - 2 sin x + 3 cos x

3 cos x - 2 sin x

38.

Select the correct derivative of:

y = 3x^-½

(3/2) x ^3/2

(-3/2) x ^-3/2

-1.5 x^1/2

(-2/3) x ^-3/2

39.

Find the derivative of the given equation
f(x) = x³ + x² + 3

3x² + 2x

3x + 2x

3x + 2x + 3

x³ + x²

40.

Find the derivative of f(x) = 6x³⁰-2x¹⁵ + 4x³ - 2x + 1

f'(x) = 18x²⁹+ 30x¹⁵ + 12x³

f'(x) = 180x²⁹ - 30x¹⁴+ 12x²

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² - 2

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² +1

41.

What is the derivative of xⁿ?

(n-1)xⁿ

nxⁿ⁺¹

(n+1)x^n-1

nx^n-1

42.

Find the derivative of:
f(x) = -5/x⁴

-20/x⁵

20/x⁵

-20/x³

20/x³

43.

Find the derivative of:
f(x) = (x²+1)⁶

12(x² + 1)⁶

12x(x² + 1)⁶

12x(x² + 1)⁵

12(x² + 1)⁵

44.

A hypothetical cube shrinks so that the length of its sides are decreasing at a rate of 4 m/min. At what rate is the volume of the cube changing when the sides are 5 m each?

-296 m³/min

-297 m³/min

-300 m³/min

-307 m³/min

45.

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in?

-262π in³/sec

-247π in³/sec

-256π in³/sec

-263π in³/sec

46.

Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 10 cm?

86π cm²/min

89π cm²/min

80π cm²/min

71π cm²/min

47.

8x⁴ -60x²

16x⁴

(8x⁴ -60x²)/(2x²-5)²

48.

Differentiate:
f(x) = x⁷ (5 + 8x)³

f '(x) = x² (5 + 8x)⁶ (35 + 80x)

f '(x) = x⁶ (5 + 8x)² (35 + 80x)

f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)

f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

49.

h=-16h²+16t+12

h=-16h²+12t+16

h=-16h²+16t

h=16h²+16t+12

50.

a)-90 f/sec b)-64 , -96 f/sec c)7.89sec d)-188.5 f/sec

a)-80 f/sec b)-64 , -96 f/sec c)5.89sec d)288.5 f/sec

a)-80 f/sec b)64 , 96 f/sec c)5.89sec d)-188.5 f/sec

a)-80 f/sec b)-64 , -96 f/sec c)5.89sec d)-188.5 f/sec

51.

Given that f(x) = x² - 3x, which of the following represents f(x + h)

x² - 3x + h

x + h² - 3x + h

(x + h)² - 3(x + h)

x² + h - 3x + h

52.

What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=0?

y+1=2(x+1)

y=2x-1

y=2x+2

y= -x-1

53.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

1/2

-2

-1/2

54.

f(x) = 2x² + 12x + 16

What is the instantaneous rate of change of f(x) at x=-3 and x=-2.

f '(-3) = 3 and f '(-2) = 0

f '(-3) = 0 and f '(-2) = 4

f '(-3) = -2 and f '(-2) = 0

f '(-3) = 1 and f '(-2) = 5

55.

What is the equation of the line normal to f(x)=5x⁵-2x at x =-1?

y+3=23(x+1)

y+3=-1/23 (x+1)

y-7=-1/23 (x+1)

y-7=-27(x+1)

56.

At the turning point. The dy/dx is.....

= 0

> 0

< 0

= 1

57.

A dam with a capacity of 900,000 litres is being filled at a rate given by V = 150t, where t is measured in minutes and V in litres. The tank will be filled in:

5000 hours

83 hours and 20 minutes

8 hours and 20 minutes

100 hours

58.

For the position function x(t) = 2t² + 3t - 3, t ∈ [0, 10], the starting and finishing positions respectively are:

-3 and 33

-3 and 63

-3 and 227

0 and 39

59.

A ball was thrown vertically upwards and the height, s metres, it reached after t seconds was given by s=28t−16t² The greatest height reached by the ball was

12¼m

14⅛m

16¾m

10½m

60.

The function y=x³+5x²−8x has

a local minimum when x=−4 and a local maximum when x=2/3

a local maximum when x=−4 and a local minimum when x=2/3

a local maximum when x=4 and a local minimum when x=−2/3

a stationary point of inflection when x=−4 and a local maximum when x=2/3

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Differentiation - Sum, Diff, Chain Rules and First Principle

Total questions: 60

Worksheet time: 2hrs 26mins

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