Free Printable Calculus Derivative Practice

1.

What is the derivative of sin(x)?

a)

sin(x)

b)

cos(x)

c)

-sin(x)

d)

-cos(x)

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
g(x) = 6 + ⅔x

a)

6

b)

12

c)

6 + ⅔

d)

⅔

4.

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

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

5.

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

a)

1/2x

b)

-2x

c)

2x

d)

-2x^-3

6.

Solve f '(2) for
f(x) = x² + 2x

a)

2x + 2

b)

6

c)

12

d)

2x

7.

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

8.

Differentiate f(x) =(2/ x⁵) - 5.

a)

x⁵-3

b)

-10x⁶

c)

x⁵-5

d)

-10x^-6

9.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

actual height

d)

intended height

10.

What is the derivative of sec(x)?

a)

sec(x)tan(x)

b)

csc(x)cot(x)

c)

-sec(x)tan(x)

d)

-csc(x)cot(x)

11.

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

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.

Find the derivative.
f(z) = 1/(3z²) + 4z³

a)

f'(z) = 6z³ + 12z²

b)

f'(z) = 6z + 12x²

c)

f'(z) = -2/(3z³) + 12z²

d)

f'(z) = -6/z² + 12z²

14.

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

a)

v = 0

b)

v = 1

c)

v = -1

d)

v = -2

15.

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)

16.

The position of an object is given as a function of time by x = 3t² + 5t³- 2t
What is the acceleration of the object at time t = 2 s?

a)

64 m/s/s

b)

60 m/s/s

c)

66 m/s/s

d)

70 m/s/s

17.

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

18.

At which x-value is f continuous but not differentiable?

a)

a

b)

b

c)

c

d)

d

19.

d/dx (sin²x) = ?

a)

2sin x

b)

2(sin x)(cos x)

c)

2cos x

d)

2x(cos x)

20.

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)

21.

Find y' if y=e^3x

a)

e^3x

b)

e^2x

c)

0

d)

3e^3x

22.

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)

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

23.

Find the first derivative of the function $f\left(x\right)=\frac{4}{\sqrt{x+4}}$

a)

$\frac{-2}{\sqrt{x+4}}$

b)

$\frac{2}{\sqrt{x+4}}$

c)

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

d)

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

24.

Given that $y=3x^7e^{-6}$ , determne $\frac{\text{d}y}{\text{d}x}$

a)

$-126x^6e^{-7}$

b)

$-126x^6e^{-5}$

c)

$21e^{-6}x^6$

d)

$21x^6e^6$

25.

What is $\frac{\text{d}}{\text{d}v}\left(\frac{v^4+4v^3-1}{v^2}\right)$ ?

a)

$2v+\frac{2}{v^3}+4$

b)

$2v+4-\frac{2}{v^3}$

c)

$\frac{4v^3+12v^2-v}{2v}$

d)

$2v^2+6v-\frac{1}{2}$

Calculus Derivative Practice

Total questions: 25

Worksheet time: 2hrs 5mins

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