Free Printable Derivatives

1.

Find the derivative of the given equation
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

2.

Find the derivative of the given equation
f(x) = -4x

a)

4

b)

x

c)

-4

d)

0

3.

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

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

4.

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

5.

find

a)

y = 2 x^-1

b)

y=2 x^-2

c)

y= −2x^-2

d)

y= −2 x^-1

6.

Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

a)

y = 500x + 400

b)

y = 100x + 400

c)

y = -500 x - 400

d)

y = 500x - 400

7.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

8.

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)

9.

What is the derivative?

a)

A

b)

B

c)

C

d)

D

10.

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

a)

6x³ - 8x²

b)

18x² - 16x

c)

15x²- 6x

d)

6x - 4

11.

.

a)

(3x²-2)cos(x³-2x)

b)

-(3x²-2)cos(x³-2x)

c)

cos(2x²-2)

d)

sin(2x²-2)

12.

Find the derivative
f(t) = (t² + 2t)⁵

a)

f'(t) = 5(2t+2)⁴

b)

f'(t) = 5(t² + 2t)⁴

c)

f'(t) = 5(t² + 2t)⁴(2t)

d)

f'(t) = 5(t² + 2t)⁴(2t + 2)

13.

f(x)= 9/∛x
f'(x) =

a)

9x^-1/3

b)

-3x^-4/3

c)

-9x^2/3

d)

-3x^2/3

14.

a)

A

b)

B

c)

C

d)

D

15.

a)

A

b)

B

c)

C

d)

D

16.

What is f'(x) if f(x) = cos(5x⁴)?

a)

f'(x) = sin(20x³)

b)

f'(x) = 20x³ sin(5x⁴)

c)

f'(x) = -sin(20x³)

d)

f'(x) = -20x³ sin(5x⁴)

17.

Find the derivative of
$f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$

a)

$-2x^2-x+9$

b)

$-2x^3-x^2+9x$

c)

$-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2$

d)

$-2x^4-x^3+9x^2$

18.

Find the second derivative of the function $f\left(x\right)=2x-5x^6$

a)

$2-30x^5$

b)

$x^2-\frac{5}{7}x^7$

c)

$-30x^5$

d)

$-150x^4$

19.

Which of the following is the derivative of $y=\left(3x^4-7\right)\left(5x^2+1\right)$

a)

$\left(12x^3\right)\left(10x\right)$

b)

$\left(3x^4-7\right)\left(10x\right)+\left(12x^3\right)\left(5x^2+1\right)$

c)

$\left(3x^4-7\right)\left(10x\right)-\left(12x^3\right)\left(5x^2+1\right)$

d)

$\frac{3x^4-7}{10x}+\frac{12x^3}{5x^2+1}$

20.

Find the derivative of
$f\left(x\right)=x^4\sin\left(x\right)$

a)

$x^4\cos\left(x\right)-4x^3\sin\left(x\right)$

b)

$x^4\cos\left(x\right)+4x^3\sin\left(x\right)$

c)

$4x^3\cos\left(x\right)$

d)

$-4x^3\cos\left(x\right)$

21.

Find the derivative of
$g\left(x\right)=\frac{3x-2}{x^2+2}$

a)

$\frac{3}{2x}$

b)

$\frac{3\left(x^2+2\right)}{\left(x^2+2\right)^2}$

c)

$\frac{-3x^2+4x+6}{\left(x^2+2\right)^2}$

d)

$\frac{9x^2-4x+6}{\left(x^2+2\right)^2}$

22.

Choose the best rule to derive the function.

a)

Product rule

b)

Quotient rule

c)

Power rule

d)

Chain rule

23.

At which point(s) will the slopes of the tangent line are zero?

a)

at C only

b)

at points A, C and E only

c)

at point B and D only

d)

at points A and E only

24.

Let f(x) = (x - 1)(x + 2). Find f'(0)

a)

0

b)

1

c)

2

d)

3

25.

At what point will the slope of y = -x² + 4 is zero?

a)

(0, 4)

b)

(1, 4)

c)

(4, 0)

d)

(1, 0)

26.

What is the slope of the line normal to the curve y = x² + x at x = 1?

a)

-1

b)

-1/2

c)

-1/3

d)

-1/4

27.

What is the equation of the line tangent to the curve y = x² at x = 1?

a)

y = 2x + 1

b)

y = 2x - 1

c)

y = -2x + 1

d)

y = x - 1

28.

What is the derivative of f?

a)

1/(x - 1)^-1

b)

-1/(x - 1)^-2

c)

-1/(x - 1)

d)

-1/(x - 1)²

29.

What is the equation of the line tangent to the curve y = -x² + 3 at (1, 2)?

a)

y = 2x - 4

b)

y = -2x - 4

c)

y = -2x + 4

d)

y = 2x + 4

30.

Find the slope of the tangent line to
f(x) = -3x²- 6x
at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

31.

What is the derivative of sin(x)?

a)

-sin(x)

b)

-cos(x)

c)

cos(x)

d)

sin(x)

32.

What is the derivative of cos(x)?

a)

sin(x)

b)

-sin(x)

c)

cos(x)

d)

-cos(x)

33.

a)

0

b)

10

c)

-10

d)

5

34.

a)

0

b)

1

c)

-32/3

d)

32/3

35.

3

a)

infinity

b)

-1/9

c)

0

d)

1/9

36.

a)

0

b)

-1

c)

1

d)

3

37.

a)

-1

b)

0

c)

3/2

d)

-3/2

38.

a)

15x²

b)

(5/4)x⁴

c)

indeterminate

d)

∞

39.

$\lim_{x\rightarrow0}\frac{6x^2-7x}{3x^2-x}\ =\ ...$

(a)

40.

$\lim_{y\rightarrow-2}\frac{y^2+5y+6}{y+2}=...$

a)

1

b)

-1

c)

9

d)

-9

41.

12

a)

-1

b)

0

c)

1

d)

pi/4

e)

nonexistent

Derivatives

Total questions: 41

Worksheet time: 1hrs 29mins

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