Free Printable Derivatives and Antiderivatives-Quiz-Review

1.

FInd the derivative:
$f\left(x\right)=4x^3-2x+1$

a)

$12x^2-2$

b)

$x^4-x^2$

c)

$x^4-x^2+x$

d)

$12x-2$

e)

None of the above

2.

Find the derivative:
$y=5+e^{4x}$

a)

$e^{4x}$

b)

$5e^{4x}$

c)

$4e^{4x}$

d)

$4e^x$

e)

None of the above

3.

Find the derivative:
$y=6\sqrt{x}$

a)

$\frac{6}{\sqrt{x}}$

b)

$\frac{12}{\sqrt{x}}$

c)

$4x^{1.5}$

d)

$\frac{1}{3\sqrt{x}}$

e)

None of the above

4.

FInd the antiderivative:
$f\left(x\right)=4x^3-2x+1$

a)

$12x^2-2+C$

b)

$x^4-x^2+C$

c)

$x^4-x^2+x+C$

d)

$12x-2+C$

e)

None of the above

5.

Find the anti-derivative:
$f\left(x\right)=\frac{1}{x^2+1}$

a)

$\ln\left(1+x^2\right)+C$

b)

$\frac{1}{2x}\ln\left(1+x^2\right)+C$

c)

$2x\tan^{-1}x+C$

d)

$\tan^{-1}x+C$

e)

None of the above

6.

∫(4 - 18x)dx

a)

F(x) = -18

b)

F(x) = 4x - 9x²

c)

F(x) = 4x - 9x²+ C

d)

F(x) = (4 - 18x)² /2 + C

7.

∫ t⁶ dt

a)

6t⁵

b)

6t⁵ + C

c)

1/7 t⁷ + C

d)

t⁷ + C

8.

∫ 1/x dx

a)

ln x

b)

ln x + C

c)

-1/x²

d)

-1/x² + C

9.

f'(x) = (x + 2)/(3x). f(x) =

a)

(2/3)ln|x| + x/3 + C

b)

2ln|3x| + x/3 + C

c)

(2/3)ln|x| + C

d)

(2/3)ln|3x| + C

10.

Given v(t) = x^-9, find the general equation for the antiderivative.

a)

(1/8)x^-8 + C

b)

(-1/8)x^-8+ C

c)

(1/10)x¹⁰

d)

(-1/8)x^-8

11.

The derivative of

a)

y'=2x-x^-2

b)

y'=x^-1+8x

c)

y'=x^-2+8x

d)

y=8x-x^-2

12.

∫(x² + x) dx

a)

2x+1 + C

b)

2x+1+C

c)

x³⁄3 + x²⁄2 + C

d)

x³⁄3 + x²⁄2 + C

13.

∫ ∜(x³) dx

a)

(4⁄7)x^7/4

b)

(4⁄7)x^7/4 + C

c)

(3/7)x^7/3 + C

d)

(1/7)x^1/7

14.

The position function x(t)=7t²-18t-7 is given. What is the velocity function?

a)

v(t)=14t-18

b)

v(t)=14t+18

c)

v(t)=18t-14

d)

v(t)=18t+14

15.

Find the derivative:
y = 3ln(x²-3)

a)

6x/(x²-3)

b)

3/(x²-3)

c)

3x/(x²-3)

d)

9x/(x²-3)

16.

Another word for 'integral' is .. .

a)

Constant

b)

Derivative

c)

Antiderivative

d)

Theorem

17.

For the function f(x)= x³- 4x²- 4x +16: Find the point(s) of inflection of the function.

a)

1

b)

4/3

c)

3/4

d)

1/2

18.

Evaluate: $\int\frac{5x-1}{x^2-3x-40}dx$

a)

$3\ln\left|x-8\right|+2\ln\left|x+5\right|+c$

b)

$4\ln\left|x-8\right|-2\ln\left|x+5\right|+c$

c)

$\ln\left|3\left(x-8\right)+2\left(x+5\right)\right|+c$

d)

$3\ln\left|x+8\right|+2\ln\left|x-5\right|+c$

19.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

20.

Evaluate: $\int_2^∞\frac{dx}{x^{2\ }}$

a)

$\frac{1}{2}$

b)

$\ln2$

c)

1

d)

3

e)

divergent

21.

Evaluate $\int_{-2}^2\ \frac{1}{1+x}dx$

a)

diverges

b)

0

c)

$\frac{1}{2}\ln3$

d)

$\frac{8}{9}$

e)

ln3

22.

Find the derivative of g(x)=(3x-2)/(x²+2)

a)

9x²+2

b)

3(x²+2)/(x²+2)²

c)

(-3x²+4x +6)/(x²+2)²

d)

(-3x²+10)/(x²+2)²

23.

$\int\frac{dx}{x^2+2x-15}$

a)

$\frac{1}{8}\ln\left|x-3\right|-\frac{1}{8}\ln\left|x+5\right|+c$

b)

$\frac{1}{4}\ln\left|x-3\right|-\frac{1}{8}\ln\left|x+5\right|+c$

c)

$\frac{1}{8}\ln\left|x+5\right|-\frac{1}{8}\ln\left|x-3\right|+c$

d)

$\frac{1}{4}\ln\left|x+5\right|-\frac{1}{4}\ln\left|x-3\right|+c$

24.

Evaluate: $\int_0^∞x^2e^{-x^3}dx$

a)

$-\frac{1}{3}$

b)

1

c)

$\frac{1}{3}$

d)

divergent

25.

Given v(t) = x^-9, find the general equation for the antiderivative.

a)

(1/8)x^-8 + C

b)

(-1/8)x^-8+ C

c)

(1/10)x¹⁰

d)

(-1/8)x^-8

26.

∫ 4 dx

a)

0

b)

4t + C

c)

4x + C

d)

2x² + C

27.

Find the antiderivative of
x²

a)

(1/3)x³+C

b)

x³

c)

(1/3)x³

d)

2x

28.

∫ t⁶ dt

a)

6t⁵

b)

6t⁵ + C

c)

1/7 t⁷ + C

d)

t⁷ + C

29.

$\int_{ }^{ }2x\ dx$

a)

$x^2\ +c$

b)

$2x^2\ +c$

c)

2+c

d)

$\frac{x}{2}+c$

30.

$\int_{ }^{ }3x^2+4x\ dx$

a)

$x^3+4x^2+c$

b)

$x^3+2x^2+c$

c)

$\frac{3}{2}x^3+4x^2+c$

d)

$3x^3+4x^2+c$

31.

$\int6x^4+3x^2+5x\ +5\ dx$

a)

$5x^5+3x^4+5x^2\ +5x$

b)

$5x^5+3x^3+5x^2\ +5x$

c)

$\frac{6}{5}x^5+x^3+5x^2\ +5x\ +c$

d)

$\frac{6}{5}x^5+x^3+\frac{5}{2}x^2\ +5x\ +c$

32.

$\int2x^{-2}dx$

a)

$2x^{-1}+c$

b)

$\frac{2}{3}x^{-3}+c$

c)

$-2x^{-1}+c$

d)

$-\frac{2}{3}x^{-3}+c$

33.

$\int_{ }^{ }7\ dx$

a)

0

b)

7+c

c)

7x+c

d)

-7x+c

34.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

slope of the secant line

d)

the function’s value

35.

Using this graph of f’(x), find the slope of the line tangent to f(x) at point c

a)

0

b)

1

c)

-1

d)

Not enough information

36.

When we "take the derivative" of a function what are we finding?

a)

What's a derivative?

b)

The rate at which our struggles in Calculus are increasing.

c)

The slope of the secant line

d)

The slope of the tangent line

37.

Find the slope at x = 3 of the equation f(x) = 3x²

a)

6x

b)

27

c)

18

d)

3x

38.

Find the slope of the Normal line to: $f\left(x\right)\ =\ \frac{4\sqrt{x}}{5}$
at x = 16

a)

$\frac{2}{5}$

b)

$-\frac{1}{160}$

c)

$\frac{1}{10}$

d)

$-10$

39.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

40.

What is the derivative of f(x)= cx?

a)

c

b)

x

c)

1

d)

0

41.

Differentiate y= x³ + 2x

a)

3x³+2x

b)

3x²+2

c)

3x+2

d)

3x

42.

What is the derivative of a constant, C?

a)

C

b)

1

c)

0

43.

find

a)

y = 2 x^-1

b)

y=2 x^-2

c)

y= −2x^-2

d)

y= −2 x^-1

44.

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

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

45.

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

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

46.

Find the derivative of the given equation
f(x) = 1/x²

a)

1/2x

b)

-2x

c)

2x

d)

-2x^-3

47.

Find the derivative of the given equation
f(x) = 1 - x²

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

48.

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

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

49.

How many derivatives can you take of a function?

a)

only 3

b)

only 2

c)

only 1

d)

until you can no longer derive it

50.

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

a)

f'(x) = 18x²⁹+ 30x¹⁵ + 12x³

b)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x²

c)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² - 2

d)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² +1

51.

Find the derivative. f(x) = 1/(3x²) + 4x³

a)

f'(x) = 6x³ + 12x²

b)

f'(x) = 6x + 12x²

c)

f'(x) = -2/(3x³) + 12x²

d)

f'(x) = -6/x² + 12x²

52.

Find the derivative f(x) = (3x + 5)⁴

a)

f'(x) = 12(3x)³

b)

f'(x) = 12(3x + 5)³

c)

f'(x) = (3)⁴

d)

f'(x) = (3x + 5)³

53.

Find the derivative f(x) = xe^x

a)

f'(x) = e^x

b)

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

c)

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

d)

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

54.

Find the derivative f(x) = x²/e^x

a)

f'(x) = (x²e^x - 2xe^x) / (e^x)²

b)

f'(x) = (2xe^x + x²e^x) / (e^x)²

c)

f'(x) = (2xe^x - x²e^x) / (e^x)²

d)

f'(x) = x²e^x + 2xe^x

55.

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

a)

(12x³)*(10x)

b)

(3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

c)

(3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

d)

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

56.

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

a)

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

b)

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

c)

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

d)

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

57.

How many derivatives can you take of a function?

a)

only 3

b)

only 2

c)

only 1

d)

until you can no longer derive it

58.

Which of the following is the quotient rule for derivatives?

a)

h^'(x)=((g(x)f^'(x) + f(x)g^'(x)) / (g(x))²

b)

h^'(x)=((g^'(x)f^'(x) - f(x)g(x)) / (g(x))

c)

h^'(x)=((g(x)f^'(x) - f(x)g^'(x)) / (g(x))²

d)

h^'(x)=((g^'(x)f^'(x) + f(x)g(x)) / (g(x))

59.

Find dy/dx by Implicit Differentiation
xy = 6

a)

-x/ y

b)

-y/ x

c)

-6y/ x

d)

y/x

60.

The acceleration function is the first derivative of...

a)

position

b)

velocity

c)

calculus

d)

particle motion

Derivatives and Antiderivatives-Quiz-Review

Total questions: 60

Worksheet time: 2hrs 11mins

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