$5 \sec x \tan^2 x + 5 \sec^3 x$

Question 1

Which of the following is the correct derivative of $y = \sin x$?

Accepted Answer

$\cos x$

Question 2

Find the derivative of $y = 3\cos x + 5\sin x$.

Accepted Answer

$-3\sin x + 5\cos x$

Question 3

Which of the following is the derivative of $y = 	an x$?

Accepted Answer

$\sec^2 x$

Question 4

A medical device rotates at an angle $x$ (in radians) and its position is given by $y = \sin x \cos x$. What is $\frac{dy}{dx}$?

Accepted Answer

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

Question 5

Find the derivative of $y = 3x - \csc x$.

Accepted Answer

$3 + \csc x \cot x$

Question 6

A chemical reaction's rate is modeled by $y = e^x \sin x$. What is $\frac{dy}{dx}$?

Accepted Answer

$e^x \sin x + e^x \cos x$

Question 7

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

Accepted Answer

$\sec x 	an x$

Question 8

A satellite's signal strength is modeled by $y = \frac{5 \cos x}{7 - 6 \cos x}$. What is $\frac{dy}{dx}$?

Accepted Answer

$\frac{-35 \sin x}{(7 - 6 \cos x)^2}$

Question 9

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

Accepted Answer

$-\csc^2 x$

Question 10

A sound wave's amplitude is given by $y = x \cos x$. What is $\frac{dy}{dx}$?

Accepted Answer

$\cos x - x \sin x$

Question 11

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

Accepted Answer

$-\csc x \cot x$

Question 12

A physics experiment models velocity as $y = \frac{x \cos x}{3 + \sin x}$. What is $\frac{dy}{dx}$?

Accepted Answer

$\frac{3 \cos x + \cos x \sin x - 3x \sin x - x \sin^2 x - x \cos^2 x}{(3 + \sin x)^2}$

Question 13

Find the second derivative of $y = 5 \sec x$.

Accepted Answer

$5 \sec x 	an^2 x + 5 \sec^3 x$

Question 14

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

Accepted Answer

$-\sin x$

Question 15

A pendulum's displacement is modeled by $y = \sin x + \cos x$. What is $\frac{dy}{dx}$?

Accepted Answer

$\cos x - \sin x$

Question 16

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

Accepted Answer

$\sec x 	an^2 x + \sec^3 x$

Question 17

A real-world signal is modeled by $y = 5 \cos x$. What is $\frac{dy}{dx}$?

Accepted Answer

$-5 \sin x$

Question 18

Find the derivative of $y = \sin x \cos x$ using the product rule.

Accepted Answer

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

Question 19

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

Accepted Answer

$\sec^2 x$

Derivatives of Trigonometric Functions: 3.5

Study Guide - Practice Questions