Free Printable Derivative Test Review

Worksheets

Derivative Test Review

Total questions: 41

Worksheet time: 3hrs 20mins

Name

Class

Date

Find the derivative:
y = 3ln(x²-3)

6x/(x²-3)

3/(x²-3)

3x/(x²-3)

9x/(x²-3)

Find the derivative f(x) = xe^x

f'(x) = e^x

f'(x) = xe^x + xe^x

f'(x) = e^x - xe^x

f'(x) = e^x + xe^x

f(x) = ln x

f '(x) = x

f '(x) =e^x

f '(x) =lnx

f '(x) = 1/x

f(x) = e^x

e^x

ln x

f (x) =e^3x

f '(x) =6e^x

f '(x) =3e^3x

f '(x) =3e^2x

f '(x) =e^3x

d/dx(e^sinx) =

e^sinx

-e^sinx(cosx)

e^sinx(cosx)

e^cosx

Find the derivative:
y=4e^x²

y'=8xe^x

y'=8xe^x²

y'=8xe^2x

y'=8xe^4x²

d/dx ln(x³)

3/x

1/x³

ln(3x²)

1 / 3x²

find the derivative of the following: ln(3x²-5x) ?

(6x-5)/(3x²-5x)

6x-5

(x³/3)-(5x²)/2

(6x-5)/(3x³-2x)

10.

d/dx(2^3x+4)

3(ln2)(2^3x+4)

3(2^3x+4)

3(2^3x+4/(ln2))

2^3x+4

11.

Find the derivative:

y=log₉x

y′=1 /((log9)x)

y′=(ln9)/x

y′=1/(x(lnx))

y′=1/((ln9)x)

12.

Find the derivative

13.

Find f'(2)

14.

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

6x³ - 8x²

18x² - 16x

15x²- 6x

6x - 4

15.

Which rule would you need to use?

Power Rule

Product Rule

Quotient Rule

Chain Rule

16.

17.

Find h'(3)

-2

18.

Where is the graph continuous yet NOT differentiable?

x = a, b, c, d

x = b, c, d

x = a, b,

x = b, d

19.

I only

I and II Only

I, II, and III

II Only

20.

Find f'(x)

21.

A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction?

6.5

22.

Find dy/dx

23.

f' is given, which could be f?

24.

Where is the graph not differentiable?

x = -2, -1, 0, 1

x = -2, -1, 1

x = -2, -1

x = -1,

25.

Find the second derivative of f(x) = x²+ e^x - cosx

f"(x) = 2 + e^x + cosx

f"(x) = 2x + e^x + cosx

f"(x) = 2x + xe^x - cosx

f"(x) = 2x + e^x + sinx

26.

Average Rate of Change

Average Value of f

Intermediate Value Theorem

Rolle's Theorem

27.

position

velocity

acceleration

total distance

28.

Which of the following are synonyms for find the derivative?

f'(x)

dy/dx

slope of the tangent line

instantaneous rate of change

29.

Given u(x) = f(x)g(x), f(2) = 3, g(2) = -3, f '(2) = 5, and g'(2) = 1,

then u'(2) = ?

-12

30.

A particle's speed is decreasing if

it's acceleration is positive

it's velocity is positive

it's velocity and acceleration have the same sign

it's velocity and acceleration have different signs

31.

An objects distance from its starting point at time t is given by the equation

s(t) = t³ - 6t² - 4.

What is the speed of the object when its acceleration is 0?

-24

32.

find y'

33.

Evaluate the derivative at

x = π

-1 - 3/(π³)

9/(π⁴)

3/(π⁴)

34.

(3x²-2)cos(x³-2x)

-(3x²-2)cos(x³-2x)

cos(2x²-2)

sin(2x²-2)

35.

During which interval is the object speeding up?

A to B

B to C

D to E

E to F

36.

If velocity is negative and acceleration is positive, then speed is ______________?

decreasing

increasing

constant

none of the above

37.

If s(t) represents the velocity graph, when is the object moving to the left?

(0, 3) U (8, 12)

(0, 7) ∪ (10, 12)

(0, 6) ∪ (10, 12)

(3, 8)

38.

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

39.

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

Velocity = 0

Velocity = 1

Velocity = -1

Velocity = -2

40.

s(t) = t² - 20
Find the average velocity from t = 3 to t = 5.

41.

Reset

Derivative Test Review

Total questions: 41

Worksheet time: 3hrs 20mins

Similar Resources on Wayground