Chapter 3.5, Problem 7E

To determine

To find: $\frac{dy}{dx}$ use the grapher to support your analysis if you are unsure to your answer.

Answer to Problem 7E

  $\frac{dy}{dx}=\frac{4\sin x}{{\cos }^{2}x}$ .

Explanation of Solution

Given information:Given equation is $y=\frac{4}{\cos x}$ .

Calculation:Given equation is $y=\frac{4}{\cos x}$ .

  $\begin{array}{l}y=\frac{4}{\cos x}\\ \frac{dy}{dx}=\frac{\cos x\frac{d}{dx}(4)-4\frac{d}{dx}({\cos }^{2}x)}{{\cos }^{2}x}\\ \frac{dy}{dx}=\frac{\cos x(0)-4(-\sin x)}{{\cos }^{2}x}\\ \frac{dy}{dx}=\frac{4\sin x}{{\cos }^{2}x}\end{array}$

Graph is: