Free Printable rules of differentiation

1.

$\frac{\text{d}}{\text{d}x}\left[\left(2x+1\right)\left(5x-4\right)\right]$

a)

$10x-3$

b)

$20x-4$

c)

$10x-4$

d)

$20x-3$

2.

$\frac{\text{d}}{\text{d}x}\left[\left(x^2-1\right)\left(x+7\right)\right]$

a)

$3x^2-14x-1$

b)

$3x^2+14x-1$

c)

$3x^2-14x+1$

d)

$3x^2+14x+1$

3.

$\frac{\text{d}}{\text{d}x}\left[\left(\sqrt{x}\right)\left(x-1\right)\right]$

a)

$\frac{3}{2}x^{\frac{1}{2}}+\frac{1}{2}x^{\frac{-1}{2}}$

b)

$\frac{3}{2}x^{\frac{1}{2}}-\frac{1}{2}x^{\frac{-1}{2}}$

c)

$\frac{1}{2}x^{\frac{1}{2}}-\frac{3}{2}x^{\frac{-1}{2}}$

d)

$\frac{1}{2}x^{\frac{1}{2}}+\frac{3}{2}x^{\frac{-1}{2}}$

4.

$\frac{\text{d}}{\text{d}x}\left[x^2\cdot\sin\left(x\right)\right]$

a)

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

b)

$-x^2\sin\left(x\right)+2x\cos\left(x\right)$

c)

$x^2\sin\left(x\right)+2x\cos\left(x\right)$

d)

$x^2\cos\left(x\right)+2x\sin\left(x\right)$

5.

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

6.

Given that y = (x+2)/(x-3), find y'.

a)

y' = -1/(x-3)²

b)

y' = -5/(x-3)²

c)

y' = (2x-5)/(x-3)²

d)

y' = (2x-1)/(x-3)²

7.

$\frac{d}{dx}\left(\frac{2}{3}x+1\right)$

Find the derivative.

a)

$1$

b)

$\frac{1}{2}$

c)

$\frac{2}{3}$

d)

$\frac{5}{3}$

8.

$f\left(x\right)=4x^3-3x^2+\sqrt{2}x$ , find its derivative.

a)

$f'\left(x\right)=12-6x$

b)

$f'\left(x\right)=12x^2-6x+\sqrt{2}$

c)

$f\left(x\right)=12x^2-6x+\sqrt{2}$

d)

$f'\left(x\right)=3x^4-2x^3+x$

9.

Find the derivative of f(x)=(x³-2x)²

a)

6x⁵ - 12x³+8x

b)

6x⁵ - 16x³+8x

c)

x⁶-4x⁴+4x²

d)

6x⁵ - 16x^3-8x

10.

find y' for y=(e^5x)+1

a)

5e^5x+1

b)

e^5x

c)

5e^5x

d)

1

11.

Differentiate:
f(x) = x⁷ (5 + 8x)³

a)

f '(x) = x² (5 + 8x)⁶ (35 + 80x)

b)

f '(x) = x⁶ (5 + 8x)² (35 + 80x)

c)

f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)

d)

f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

12.

$\frac{\text{d}}{\text{d}x}\left[x^2\left(x+1\right)\left(2x-3\right)\right]$

a)

$8x^3-3x^2-6x$

b)

$8x^3+3x^2-6x$

c)

$8x^3-3x^2+6x$

d)

$8x^3+3x^2+6x$

13.

$\frac{\text{d}}{\text{d}x}\left[\frac{1}{x}\cdot\frac{1}{2x^2}\cdot\frac{-1}{3x^3}\right]$

a)

$\frac{1}{x^6}$

b)

$-\frac{1}{x^7}$

c)

$\frac{-1}{x^6}$

d)

$\frac{1}{x^7}$

14.

Given $f\left(x\right)=3x^2+2x-1$ , which of the following is the correct derivative?

a)

$f'\left(x\right)=6x^2+2$

b)

$f'\left(x\right)=6x+2$

c)

$f'\left(x\right)=6x^2+2$

d)

$f'\left(x\right)=6x^2+2x^2-x$

15.

Given $f\left(x\right)=17$ , what is the derivative of $f\left(x\right)$ ?

a)

$f'\left(x\right)=17x$

b)

$f'\left(x\right)=17$

c)

$f'\left(x\right)=0$

d)

$f'\left(x\right)=17x^2$

16.

Differentiate with respect to x. $y=\frac{1}{x^3}$

a)

$\frac{\partial y}{\partial x}=\frac{1}{x^4}$

b)

$\frac{\partial y}{\partial x}=-3x$

c)

$\frac{\partial y}{\partial x}=-\frac{3}{x^3}$

d)

$\frac{\partial y}{\partial x}=-\frac{3}{x^4}$

rules of differentiation

Total questions: 16

Worksheet time: 1hrs 20mins

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