Free Printable Differentiation - including trigonometric functions

1.

Find the derivative of

a)

$\sin x$

b)

$-\sin x$

c)

$-\operatorname{cosec}x\cot x$

d)

$\sec2x$

2.

Find the derivative of

a)

$\operatorname{cosec}x\cot x$

b)

$\sec x\tan x$

c)

$\sec^2x$

d)

$-\operatorname{cosec}x\cot x$

3.

The derivative of $x\cos2x$

a)

$2x\sin2x+\cos2x$

b)

$-2x\sin2x+\cos2x$

c)

$\cos2x+4\sin2x$

d)

$2x\cos2x$

4.

Find $\frac{\text{d}y}{\text{d}x}$ of y = ln (6x+1)

a)

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

b)

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

c)

$\frac{1}{6x}$

d)

6

5.

Find dy/dx for $y=e^{6x}$

a)

$e^{6x}$

b)

$6e^{6x}$

c)

$e^{6x-1}$

d)

$6xe^{6x-1}$

6.

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)

$2x+1$

7.

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

a)

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

b)

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

c)

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

d)

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

8.

Differentiate $\sqrt{1-3x^2}$

a)

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

b)

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

c)

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

d)

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

9.

Find $\frac{dy}{dx}$ for $y=\tan^4\left(2x+1\right)$ .

a)

$8\tan^4\left(2x+1\right)\sec^2\left(2x+1\right)$

b)

$2\tan^3\left(2x+1\right)\sec^2\left(2x+1\right)$

c)

$4\tan^3\left(2x+1\right)\sec^2\left(2x+1\right)$

d)

$8\tan^3\left(2x+1\right)\sec^2\left(2x+1\right)$

10.

Find dy/dx for y= cos 4x

a)

dy/dx = -4 sin 4x

b)

dy/dx=sin 4x

c)

dy/dx = - 4 cos 4x

d)

dy/dx = 4 sin 4x

11.

$If\ y\ =\ \tan\left(x^4\right)\ then\ \frac{\text{d}y}{\text{d}x}=$

a)

$\tan\left(3x^4\right)\$

b)

$\sec\left(x^4\right)\tan\left(x^4\right)$

c)

$\sec^2\left(x^4\right)$

d)

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

12.

$If\ y\ =\ \sin^5\left(x\right)\ then\ \frac{\text{d}y}{\text{d}x}\ =$

a)

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

b)

$5\sin x.\cos x$

c)

$5\cos x$

d)

$5\sin^4x.\ \cos x$

13.

$If\ y\ =\ e^{\sec x}\ then\ \frac{\text{d}y}{\text{d}x}=$

a)

$\sec x\tan x.e^{\sec x}$

b)

$e^{\sec x}$

c)

$e^{\sec x.\tan x}$

d)

$\sec x.e^{\sec x-1}$

14.

$\frac{d}{dx}\sin x$

a)

$\sin\ x$

b)

$-\cos x$

c)

$-\sin\ x$

d)

$\cos x$

15.

$\frac{d}{dx}\cos x$

a)

$\sin\ x$

b)

$-\cos x$

c)

$-\sin\ x$

d)

$\cos x$

16.

$\frac{d}{dx}\ a^{x\ }=$

a)

$a^x$

b)

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

c)

$a^x\ \log_ea$

d)

$\frac{1}{x}$

17.

$\frac{d}{dx}\tan x\ =$

a)

$\sin x\ \cos x$

b)

$\sec^2x$

c)

$\sec x\ \tan x$

d)

$\frac{\sin x}{\cos x}$

18.

$\frac{d}{dx}\cot x\ =$

a)

$-\operatorname{cosec}^2x$

b)

$\cos x$

c)

$\operatorname{cosec}^2x$

d)

$\operatorname{cosec}x\ \cot x$

19.

$\frac{d}{dx}\operatorname{cosec}x$

a)

$\frac{1}{\sin x}$

b)

$\operatorname{cosec}^2x$

c)

$-\operatorname{cosec}x\ \cot x$

d)

$\operatorname{cosec}x\ \cot\ x$

20.

$\frac{d}{dx}\sec x\ =$

a)

$\sec^2x$

b)

$\frac{1}{\cos x}$

c)

$-\sec x\tan x$

d)

$\sec x\ \tan x$

21.

The derivative of sin2x with respect to x is

a)

2 cos x

b)

2 cos 2x

c)

−2 cos x

d)

-2 cos 2x

22.

The derivative of tan3x with respect to x is

a)

sec²3x

b)

tan 3x sec 3x

c)

3 sec²3x

d)

−3 sec²3x

Differentiation - including trigonometric functions

Total questions: 22

Worksheet time: 11mins

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