Free Printable Derivative practice

1.

Determine the derivative of f(x) = 6x

a)

6

b)

x

c)

6x

d)

2x²

2.

What is the derivative of g(x) = 4x³

a)

12

b)

12x²

c)

4

d)

3

3.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

4.

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

a)

7

b)

0

c)

7x

d)

14

5.

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

6.

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

7.

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

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

8.

The derivative of a function is its

a)

Slope

b)

Maximum/Minimum

c)

Instantaneous rate of change

d)

Common Denominator

9.

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

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

10.

Differentiate f(x) = 5x⁷.

a)

35x⁶

b)

210x⁵

c)

5x⁶

d)

1050x⁴

11.

y=5x²+ 3x + 9
dy/dx =

a)

10x

b)

10x+3

c)

10x²+3

d)

10

12.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

13.

Find the derivative of f(x) = 5x² + 7x - 3.

a)

2x + 7

b)

10x + 7

c)

10x + 4

d)

2x + 4

14.

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

a)

$-2x^2-x+9$

b)

$-2x^2+x+9$

c)

$2x^2-x+9$

d)

$2x^2-x-9$

15.

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

16.

Differentiate h(x) = 3x^5/3 - 6x^1/6 + 3x

a)

h'(x) = 5x^2/3 - x^-5/6 + 3

b)

h'(x) = 3x^2/3 - 6x + 3

c)

h'(x) = 5x^4/3 - 6x + 3

d)

h'(x) = 3x^4/3 - x^-5/6 + 3

17.

FInd the derivative:

f(x) = (-2/3)x³ - (1/2)x² + 9x

a)

-2x² - x + 9

b)

-2x² + x + 9

c)

2x² - x + 9

d)

2x² - x - 9

18.

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

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

19.

$f\left(x\right)=10x^{-4}-5x^{-2}+x+1$ find f'

a)

$-40x^{-3}+10x^{-1}+1$

b)

$-40x^{-5}+10x^{-3}+1$

c)

$40x^{-5}+10x^{-1}+1$

d)

$-40x^{-5}-10x^{-3}+1$

20.

$\frac{\text{d}}{\text{d}x}\left(2x^{\pi}\right)$

a)

$2\pi x^{\pi}-1$

b)

$2\pi x^{-1}$

c)

2

d)

$2\pi x^{\left(\pi-1\right)}$

e)

0

21.

What is $\frac{\text{d}}{\text{d}x}\left(\sqrt{x}-\frac{1}{x}\right)=?$ . You can choose more than ONE answer.

a)

$\frac{1}{2\sqrt{x}}-\frac{1}{x^2}$

b)

$\frac{1}{2}\sqrt{x}+\frac{1}{x^2}$

c)

$\frac{1}{2\sqrt{x}}+\frac{1}{x^2}$

d)

$\frac{1}{2}x^{-\frac{1}{2}}+\frac{1}{x^2}$

22.

$\frac{\text{d}}{\text{d}y}\left(-\frac{1}{y^3}\right)=-3y^{-4}$ is TRUE.

a)

True

b)

False

23.

Find $f'\left(x\right)$ if $f\left(x\right)=\frac{5}{x^2}$

a)

5x

b)

$\frac{5}{2x}$

c)

5x^-2

d)

$-\frac{10}{x^3}$

Derivative practice

Total questions: 23

Worksheet time: 1hrs 9mins

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