Free Printable Differentiation of Trigonometric Functions

1.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=2\cos\left(4x\right)

is

a)

-2 sin (4x)

b)

2 sin (4x)

c)

-8 sin (4x)

d)

8 sin (4x)

2.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=2\sin\left(4x\right)

is

a)

8 cos (4x)

b)

-8 cos (4x)

c)

2 cos (4x)

d)

- 2 cos (4x)

3.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=2\tan\left(4x\right)

is

a)

$2\ \sec^2x$

b)

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

c)

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

d)

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

4.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=2\cot\left(4x\right)

is

a)

$-2\ \operatorname{cosec}^2\left(4x\right)$

b)

$2\ \operatorname{cosec}^2\left(4x\right)$

c)

$-8\ \operatorname{cosec}^2\left(4x\right)$

d)

$8\ \operatorname{cosec}^2\left(4x\right)$

5.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=2\operatorname{cosec}\left(4x\right)

is

a)

$-2\ \operatorname{cosec}\left(4x\right)\cot\left(4x\right)$

b)

$2\ \operatorname{cosec}\left(4x\right)\cot\left(4x\right)$

c)

$8\ \operatorname{cosec}\left(4x\right)\cot\left(4x\right)$

d)

$-8\ \operatorname{cosec}\left(4x\right)\cot\left(4x\right)$

6.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=2\sec\left(4x\right)

is

a)

$-2\ \sec\left(4x\right)\tan\left(4x\right)$

b)

$8\ \sec\left(4x\right)\tan\left(4x\right)$

c)

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

d)

$-8\ \sec\left(4x\right)\tan\left(4x\right)$

7.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=\sin\left(2x^2\right)

is

a)

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

b)

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

c)

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

d)

$-4x\cos\left(2x^2\right)$

8.

Given $f\left(x\right)=\cos^2\left(4x\right)$ . The derivative, $f'\left(x\right)$

is

a)

$2\cos\left(4x\right)\sin\left(4x\right)$

b)

$8\cos\left(4x\right)\sin\left(4x\right)$

c)

$-8\cos\left(4x\right)\sin\left(4x\right)$

d)

$-2\cos\left(4x\right)\sin\left(4x\right)$

9.

Given $f\left(x\right)=\tan^3\left(4x^2\right)$ . The derivative, $f'\left(x\right)$

is

a)

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

b)

$12\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

c)

$24\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

d)

$24x\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

10.

Given $f\left(x\right)=\cos^5\left(2x^3\right)$ . The derivative, $f'\left(x\right)$

is

a)

$-30x^2\cos^4\left(2x^3\right)\sin\left(2x^3\right)$

b)

$-5x^2\cos^4\left(2x^3\right)\sin\left(2x^3\right)$

c)

$5x^2\cos^4\left(2x^3\right)\sin\left(2x^3\right)$

d)

$30x^2\cos^4\left(2x^3\right)\sin\left(2x^3\right)$

Differentiation of Trigonometric Functions

Total questions: 10

Worksheet time: 8mins

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