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1.

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

2.

a)

A

b)

B

c)

C

d)

D

3.

The derivative of

a)

y'=2x-x^-2

b)

y'=x^-1+8x

c)

y'=x^-2+8x

d)

y=8x-x^-2

4.

Determine the derivative.

a)

4x⁸+60x⁶+12x³

b)

12x⁷+36x²

c)

32x⁷+36x²

d)

20x⁶

5.

f(x)= 9/∛x
f'(x) =

a)

9x^-1/3

b)

-3x^-4/3

c)

-9x^2/3

d)

-3x^2/3

6.

Find the derivative.

a)

(x⁵ - 2)(4x²+1)+(5x⁴)(8x)

b)

(5x⁴)(8x)

c)

(x⁵ - 2)(8x)+(4x²+1)(5x⁴)

d)

(x⁵ - 2)(8x)-(4x²+1)(5x⁴)

7.

Find the derivative

a)

-40x⁴/(2x⁵+5)²

b)

40x⁴/(2x⁵+5)²

c)

-40x⁴/(2x⁵+5)

d)

0/(10x⁴)

8.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

slope of the secant line

9.

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

a)

3/(2x)

b)

(-3x²-4x +6)/(x²+2)²

c)

(-3x²+4x +6)/(x²+2)²

d)

(-3x²+10)/(x²+2)²

10.

Given that the position function for a particular object is given by
s(t) = t³- 3t +5, find the acceleration of the object at t = 2 seconds.

a)

27

b)

12

c)

6

d)

-2

11.

Find 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)

12.

$\frac{d}{dx}\left[\cos\left(x\right)\right]$

a)

$\sin\left(x\right)$

b)

$-\sin\left(x\right)$

c)

$\sec\left(x\right)$

d)

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

13.

$\frac{d}{dx}\left[\sec\left(x\right)\right]$

a)

$\tan\left(x\right)$

b)

$\cos\left(x\right)$

c)

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

d)

$\csc\left(x\right)\cot\left(x\right)$

14.

If f(x) = sec(4x), then f'(x) =

a)

4sec(4x)tan(4x)

b)

2sec(4x)tan(4x)

c)

-4csc(4x)cot(4x)

d)

-2csc(4x)cot(4x)

15.

If f(x) = sin³(2x), then f'(x) =

a)

3cos(2x)

b)

3sin(2x)⋅2

c)

3sin²(2x)cos(2x)

d)

3sin²(2x)cos(2x)⋅2

Welcome Back To Calculus

Total questions: 15

Worksheet time: 52mins

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