Chapter 3.5, Problem 6E

To determine

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

Answer to Problem 6E

  $\frac{dy}{dx}=3+x({\sec }^{2}x)+\tan x$ .

Explanation of Solution

Given information:Given equation is $y=3x+x\tan x$ .

Calculation:Given equation is $y=3x+x\tan x$ .

  $\begin{array}{l}y=3x+x\tan x\\ \frac{dy}{dx}=3+(x\frac{d}{dx}(tanx)+tanx\frac{d}{dx}(x))\\ \frac{dy}{dx}=3+x({\sec }^{2}x)+\tan x(1)\\ \frac{dy}{dx}=3+x({\sec }^{2}x)+\tan x\end{array}$

Graph is: