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

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

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

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