Free Printable Derivatives worksheet

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 the derivative of $y=\frac{2}{x}$

a)

y = 2 x^-1

b)

y=2 x^-2

c)

y= −2x^-2

d)

y= −2 x^-1

6.

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)

7.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

8.

Find the derivative of $y=x^4.\sin x$

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

9.

What is the derivative of ax?

a)

a

b)

x

c)

1

d)

0

10.

Differentiate y= x³ + 2x

a)

3x³+2x

b)

3x²+2

c)

3x+2

d)

3x

11.

What is the derivative of a constant, C?

a)

C

b)

1

c)

0

12.

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

13.

Find the derivative of
f(x) = $\frac{1}{x^2}$

a)

1/2x

b)

-2x

c)

2x

d)

-2x^-3

14.

Find the derivative of the given function

f(x) = 1 - x²

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

15.

Find the derivative of the given function

f(x) = x³ + x² + 3

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

16.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

17.

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

a)

6x³ - 8x²

b)

18x² - 16x

c)

15x²- 6x

d)

6x - 4

18.

Derive y = sin ( 5x ) with respect to x.

a)

$-\cos\left(5x\right)$

b)

$\cos\left(5x\right)$

c)

$5\cos\left(5x\right)$

d)

$\sec\left(5x\right)$

19.

Derive y=3x²-4x+2

a)

6x-6

b)

6x-2

c)

4-6x

d)

6x-4

20.

Differentiate f(x) = 5x⁷.

a)

35x⁶

b)

210x⁵

c)

5x⁶

d)

1050x⁴

21.

Solve f '(2) for
f(x) = x² + 2x

a)

2x + 2

b)

6

c)

12

d)

2x

22.

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

a)

$2-30x^5$

b)

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

c)

$-30x^5$

d)

$-150x^4$

23.

$\frac{d}{dx}\left[\sin\left(x^3-2x\right)\right]=$

a)

$\left(3x^2-2\right)\cos\left(x^3-2x\right)$

b)

$-\left(3x^2-2\right)\cos\left(x^3-2x\right)$

c)

$\cos\left(3x^2-2\right)$

d)

$\sin\left(3x^2-2\right)$

24.

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)

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

25.

What is the derivative of f(x) = 2x³- 4x + 5?

a)

f'(x) = 6x² - 4x

b)

f'(x) = 2/3x² - 4x

c)

f'(x) = 3x² - 4

d)

f'(x) = 6x² - 4

26.

Choose the best rule to derive the function.
$y=\sqrt{x^2+1}$

a)

Product rule

b)

Quotient rule

c)

Power rule

d)

Chain rule

27.

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

28.

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

a)

0

b)

1

c)

2

d)

3

29.

$\lim_{x\rightarrow0}\ \frac{1-Cos\ 4x}{Sin^23x}=$

a)

$\frac{2}{3}$

b)

$\frac{4}{3}$

c)

$\frac{4}{9}$

d)

$\frac{8}{9}$

30.

$f\left(x\right)=x^3+2x^2-8x\$ and $g\left(x\right)=x^2-5x+6$ Find $\lim_{x\rightarrow2}\ \frac{f\left(x\right)}{g\left(x\right)}=$

a)

6

b)

3

c)

-12

d)

-6

31.

Which of the following is / are true ?

a)

$\left(100x\right)^I\ =\ 100$

b)

$\left(\sqrt{5}\right)^I\ =\ 0$

c)

$\left(x\right)^I\ =\ 0$

32.

Which of the following is / are true ?

a)

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

b)

$\left(3x^2\right)^I\ =\ 6x$

c)

$\left(\ 5\ -x^3\right)^I\ =\ 5\ -\ 3.x^2$

33.

Which of the following is / are true ?

a)

$\left(\sin x\right)^I\ =\ -\cos x$

b)

$\left(\cos x\right)^I\ =\ -\sin x$

c)

$\left(\ \sin x+\cos x\right)^I\ =\ \cos x-\sin x$

34.

Which of the following is / are true ?

a)

$\left(\ u\ +v\right)^I\ =\ u^I\ +\ v^I$

b)

$\left(u\ -\ v\right)^I\ =\ u^I\ -\ v^I$

c)

$\left(\ u.v\right)^I\ =\ u^I.v\ +\ v^I.u$

d)

$\left(\frac{u}{v}\right)^I\ =\ \frac{u^I.v\ -\ v^I.u}{v^2}$

35.

Find the derivative of
$y\ =\ \left(2x\ +\ 3\right)^4\$

a)

$4.\left(2x+3\right)^3$

b)

$8.\left(2x\ +\ 3\right)^4$

c)

$8.\left(2x+3\right)^3$

d)

$4.\left(2x+3\right)^4$

36.

$\lim_{x\rightarrow1}\ \frac{3x^2+3x-6}{x-1}$ = ?

a)

3

b)

6

c)

9

d)

12

37.

$\lim_{x\rightarrow0}\ \frac{x^2+\sin^2x}{1\ -\cos x}$ = ?

a)

0

b)

0

c)

0

d)

0

38.

Derive y = cos ( 3x - 20) with respect to x.

a)

$-3.\cos\left(3x-20\right)$

b)

$3.\sin\left(3x\ -20\right)$

c)

$-3.\cos\left(3x-20\right)$

d)

$-3.\sin\left(3x-20\right)$

39.

Solve f ''(1) for

f(x) = x³ - 2x² + 2x -100

a)

1

b)

2

c)

3

d)

4

40.

Find the derivative of
$g\left(x\right)=\frac{\sin x}{x}$

a)

$\frac{x.\cos x-\sin x}{x^2}$

b)

$\frac{x.\sin x-\cos x}{x^2}$

c)

$\frac{x.\cos x+\sin x}{x^2}$

d)

$\frac{x.\sin x-\cos x}{2x}$

Derivatives worksheet

Total questions: 40

Worksheet time: 50mins

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