Free Printable Trig Derivatives Practice

1.

What is the derivative of cot(x)?

a)

sec²(x)

b)

-sec²(x)

c)

csc²(x)

d)

-csc²(x)

2.

What is the derivative of sin(x)?

a)

-sin(x)

b)

-cos(x)

c)

cos(x)

d)

sin(x)

3.

What is the derivative of cos(x)?

a)

sin(x)

b)

-sin(x)

c)

cos(x)

d)

-cos(x)

4.

What is the derivative of csc(x)?

a)

csc(x)cot(x)

b)

-csc(x)cot(x)

c)

-csc²(x)

d)

-cot²(x)

5.

When we "take the derivative" of a function what are we finding?

a)

What's a derivative?

b)

The rate at which our struggles in Calculus are increasing.

c)

The slope of the secant line

d)

The slope of the tangent line

6.

What is the derivative of tan(x)?

a)

-sec²(x)

b)

-csc²(x)

c)

sec²(x)

d)

csc²(x)

7.

What is the derivative of sec(x)?

a)

sec(x)tan(x)

b)

csc(x)cot(x)

c)

-sec(x)tan(x)

d)

-csc(x)cot(x)

8.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

9.

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

10.

Which problem below would require the "product rule" ?

a)

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

b)

xsinx

c)

$\sin^3x$

d)

$\sin x^{3\ }$

11.

$\frac{d}{dx}x^3\cos x=$

a)

$-3x^2\sin x$

b)

$x^3\sin x+3x^2\cos x$

c)

$-x^3\sin x+3x^2\cos x$

d)

$3x^2\sin x+x^3\cos x$

12.

$y=x-2\cos x$
Has a horizontal tangent on
$0\le x<2\pi$
at

a)

$x=\frac{\pi}{6}$ and $\frac{5\pi}{6}$

b)

$x=\frac{\pi}{3}$ and $x=\frac{2\pi}{3}$

c)

$x=\frac{4\pi}{3}$ and $x=\frac{5\pi}{3}$

d)

$x=\frac{\pi}{6}$ and $x=\frac{11\pi}{6}$

e)

$x=\frac{7\pi}{6}$ and $x=\frac{11\pi}{6}$

13.

What is the equation of the tangent line to y = cos x at x = $\frac{\pi}{3}$

a)

$y\ -\ \frac{\pi}{3}=\frac{1}{2}\left(x-\frac{1}{2}\right)$

b)

$y\ -\frac{\sqrt{3}}{2}=\frac{1}{2}\left(x\ -\ \frac{\pi}{3}\right)$

c)

$y\ -\ \frac{1}{2}=\frac{1}{2}\left(x-\frac{\pi}{3}\right)$

d)

$y\ -\frac{1}{2}=-\frac{\sqrt{3}}{2}\left(x\ -\ \frac{\pi}{3}\right)$

Trig Derivatives Practice

Total questions: 13

Worksheet time: 3hrs 15mins

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