$$\sec x \tan x \csc x - \sec x \csc x \cot x$$

Question 1

Which of the following is the correct derivative of $$\sin x$$ with respect to $$x$$?

Accepted Answer

$$\displaystyle \frac{d}{dx}(\sin x) = \cos x$$

Question 2

Find the derivative of $$y = x \cos x.$$

Accepted Answer

$$\cos x - x \sin x$$

Question 3

Which of the following is the correct derivative of $$	an x$$?

Accepted Answer

$$\sec^2$ x$$

Question 4

Evaluate $$\displaystyle \lim_{x 	o 0} \frac{\sin 4x}{x}.$$

Accepted Answer

4

Question 5

Find the second derivative of $$y = \sin x.$$

Accepted Answer

$$-\sin x$$

Question 6

Which of the following is the correct derivative of $$\sec x$$?

Accepted Answer

$$\sec x 	an x$$

Question 7

A medical device uses the function $$f(x) = \cos x to $$model a periodic signal. What is the rate of change of the signal at $$x = \frac{\pi}{2}$$?

Accepted Answer

0

Question 8

Find the derivative of $$y = \frac{1}{1 - \sin x}.$$

Accepted Answer

$$\frac{2 \cos x}{(1 - \sin x)^2$}$$

Question 9

Which of the following is the correct derivative of $$\cot x$$?

Accepted Answer

$$-\csc^2$ x$$

Question 10

Find the derivative of $$y = \sec x \csc x.$$

Accepted Answer

$$\sec x 	an x \csc x - \sec x \csc x \cot x$$

Question 11

A sound wave is modeled by $$y = \sin x. $$What is the fourth derivative $$\frac{d^4$y}{dx^4$}$$?

Accepted Answer

$$\sin x$$

Question 12

Which of the following is the correct derivative of $$\csc x$$?

Accepted Answer

$$-\csc x \cot x$$

Question 13

Evaluate $$\displaystyle \lim_{x 	o 0} \frac{\sin 3x}{\sin 5x}.$$

Accepted Answer

$$\frac{3}{5}$$

Question 14

Find the second derivative of $$y = -\csc x \cot x.$$

Accepted Answer

$$\csc x (\cot^2$ x + \csc^2$ x)$$

Question 15

Which of the following best describes the pattern of higher-order derivatives of $$y = \sin x$$?

Accepted Answer

They repeat every four derivatives.

Question 16

A pendulum's position is modeled by $$y = \cos x. $$What is the third derivative $$\frac{d^3$y}{dx^3$}$$?

Accepted Answer

$$-\cos x$$

Question 17

Which of the following is the correct derivative of $$\cos x$$?

Accepted Answer

$$-\sin x$$

Question 18

If $$y = \sin x$$, what is $$\frac{d^3$y}{dx^3$}$$?

Accepted Answer

$$-\cos x$$

Question 19

Which of the following is the correct derivative of $$\cot x$$ with respect to $$x$$?

Accepted Answer

$$-\csc^2$ x$$

Question 20

A satellite's angular position is given by $$	heta(t) = \sin t. $$What is the instantaneous rate of change of $$	heta at$$ $$t = 0$$?

Accepted Answer

1

Derivatives of Trigonometric Functions: Calculus Study Notes

Study Guide - Practice Questions