Free Printable DIFFERENTIATION

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.

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

a)

7

b)

0

c)

7x

d)

14

3.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

4.

Find the derivative of:
f(x) = 7(3x+ 4)⁵

a)

35(3x + 4)⁵

b)

35(3x + 4)⁴

c)

105(3x + 4)⁵

d)

105(3x + 4)⁴

5.

Let y = (x - 1)(x + 2). Find dy/dx.

a)

2x + 1

b)

2x - 1

c)

4x - 1

d)

2x² + x - 1

6.

Find $\frac{dy}{dx}$ for $y=\left(x+5\right)\left(2x-1\right)$ .

a)

$9-4x$

b)

$4x+9$

c)

$4x-9$

d)

$-4x-9$

7.

Find $\frac{dy}{dx}$ for $y=3x^2\left(5x+1\right)$ by using product rule.

a)

$45x^2-6x$

b)

$45x^2+6x^{-1}$

c)

$45x+6$

d)

$45x^2+6x$

8.

Find $\frac{dy}{dx}$ for $y=\frac{3x+2^{ }}{2x+1}$ by using quotient rule.

a)

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

b)

$\frac{1}{\left(2x+1\right)^2}$

c)

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

d)

$2x+1$

9.

Use the product rule to find the derivative. $f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$

a)

$-3x^2+12x^3$

b)

$-21x^3+6x$

c)

$-21x^6+6x^2$

d)

$-84x^6-6x^2$

10.

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

a)

$-6x^3-4x$

b)

$-12x^3-4x$

c)

$12x^3+4x$

d)

$-36x^2-4$

11.

a)

8x⁴ -60x²

b)

16x⁴

c)

(8x⁴ -60x²)/(2x²-5)²

d)

3x

12.

a)

b)

c)

d)

13.

a)

f '(x) =3x³ + 12/4x⁵

b)

f '(x) = 36x⁶

c)

f '(x) =16x³ - 9x²/9x⁶ + 18x³ + 9

d)

f '(x) =4x⁶ + 16x³/3x⁶ + 6x³ + 3

14.

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

15.

a)

f '(x) = -5x³/x⁸ + 2x⁴+ 1

b)

f '(x) = -80x³

c)

f '(x) = -x³/x⁸ + 2x⁴ + 1

d)

f '(x) = -16x³/5

DIFFERENTIATION

Total questions: 15

Worksheet time: 29mins

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