Free Printable trigonometric derivatives

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Worksheets

trigonometric derivatives

Total questions: 20

Worksheet time: 2hrs 40mins

Name

Class

Date

1.

Determine the derivative of: f(x) = x⁴sinx

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

2.

Find the derivative f(x) = tanxcosx

a)

f'(x) = sec²xcosx - tanxsinx

b)

f'(x) = sec²xcosx + tanxsinx

c)

f'(x) = sec²xsinx

d)

f'(x) = sec²xcosx - tanxcosx

3.

What is the derivative of -cos(x)?

a)

sin(x)

b)

-sin(x)

c)

cos(x)

d)

-cos(x)

4.

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

5.

What is the derivative of cot(x)?

a)

sec²(x)

b)

-sec²(x)

c)

csc²(x)

d)

-csc²(x)

6.

What is the derivative of tan(x)?

a)

-sec²(x)

b)

-csc²(x)

c)

sec²(x)

d)

csc²(x)

7.

What is f'(x) if f(x) = cos(5x⁴)?

a)

f'(x) = sin(20x³)

b)

f'(x) = 20x³ sin(5x⁴)

c)

f'(x) = -sin(20x³)

d)

f'(x) = -20x³ sin(5x⁴)

8.

Find g'(x) if g(x) = sin^1/2(4x)

a)

2cos^-1/2(4x)

b)

4cos^1/2(4x)

c)

2sin^-1/2(4x)cos(4x)

d)

1/2sin^-1/2(4x)cos(4x)

9.

If f(x) = -csc(x/2), then f'(x) =

a)

sec²(x/2)

b)

2csc(x/2)cot(x/2)

c)

½csc(x/2)cot(x/2)

d)

-csc²(x/2)

10.

y= sin²x find y'

a)

2sin x

b)

2(sin x)(cos x)

c)

2cos x

d)

2x(cos x)

11.

If f(x) = 4tan(½⋅x), then f'(x) =

a)

4sec²(1/2x)

b)

-4csc²(2x)

c)

2sec²(1/2x)

d)

-2csc²(1/2x)

12.

.

a)

(3x²-2)cos(x³-2x)

b)

-(3x²-2)cos(x³-2x)

c)

cos(2x²-2)

d)

sin(2x²-2)

13.

Find the derivative of f(x) = -3x⁴cscx

a)

f'(x) = 12x³cscxcotx

b)

f'(x) = -3x⁴cscxcotx

c)

f'(x) =-12x³cscx + 3x⁴cotxcscx

d)

f'(x) = -3xcosx

14.

Differentiate the function with respect to x:

y=\sin^{-1}\left(x^4\right)

a)

$\frac{dy}{dx}=\frac{4x^3}{1-x^8}$

b)

$\frac{dy}{dx}=\cos x^4\times4x^3$

c)

$\frac{dy}{dx}=\frac{4x^3}{\sqrt{1-x^8}}$

d)

$\frac{dy}{dx}=\frac{4x^3}{\sqrt{1-x^4}}$

15.

Differentiate the function with respect to x:

f\left(x\right)=\tan^{-1}\left(-5x^4\right)

a)

$f'\left(x\right)=-\frac{20x^3}{\sqrt{25x^8+1}}$

b)

$f'\left(x\right)=\sec^2\left(-5x^4\right)\times-20x^3$

c)

$f'\left(x\right)=-\frac{20x^3}{-5x^4+1}$

d)

$f'\left(x\right)=-\frac{20x^3}{25x^8+1}$

16.

Differentiate the function with respect to x:

f\left(x\right)=\sin^{-1}\left(-3x^2\right)

a)

$f'\left(x\right)=-\frac{6x}{\sqrt{1+3x^2}}$

b)

$f'\left(x\right)=-\frac{6x}{1-9x^4}$

c)

$f'\left(x\right)=-\frac{6x}{\sqrt{1-9x^4}}$

d)

$f'\left(x\right)=-\cos\left(-3x^2\right)\times-6x$

17.

Differentiate the function with respect to x:

y=\sin^{-1}\left(4x^2\right)

a)

$\frac{dy}{dx}=\cos4x^2\times8x$

b)

$\frac{dy}{dx}=\frac{8x}{1-16x^4}$

c)

$\frac{dy}{dx}=\frac{8x}{\sqrt{1-16x^4}}$

d)

$\frac{dy}{dx}=\frac{8x}{\sqrt{1-4x^2}}$

18.

Differentiate the function with respect to x:

y=\tan^{-1}\left(4x^5\right)

a)

$\frac{dy}{dx}=\frac{20x^4}{\sqrt{16x^{10}+1}}$

b)

$\frac{dy}{dx}=\frac{20x^4}{16x^{10}+1}$

c)

$\frac{dy}{dx}=\frac{20x^4}{4x^5+1}$

d)

$\frac{dy}{dx}=\sec^24x^5\times20x^4$

19.

$\frac{d}{dx}\left(x\sin x\right)=$

a)

$\cos x$

b)

$x\sin x+\cos x$

c)

$x\cos x+\sin x$

d)

$x\sin x-\cos x$

20.

.

a)

(3x²-2)cos(x³-2x)

b)

-(3x²-2)cos(x³-2x)

c)

cos(2x²-2)

d)

sin(2x²-2)

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