Chapter 4, Problem 2RE

To determine

To Find: The derivative of the given function.

Answer to Problem 2RE

The derivative is $e^x{\sec }^2(e^x)$ .

Explanation of Solution

Given information: Given function $y=\tan (e^x)$

Formula used: $\frac{d(e^x)}{dx}=e^x\text{and}\frac{d(\tan x)}{dx}={\sec }^{2}x$ with chain rule.

Calculation:

  $\begin{array}{l}y=\tan (e^x)\\ \text{Differentiate}\text{with}\text{respect}\text{to}x\\ \frac{dy}{dx}=\frac{d(\tan e^x)}{d(e^x)}\times \frac{d(e^x)}{dx}\\ \frac{dy}{dx}={\sec }^2(e^x)\times e^x\\ \frac{dy}{dx}=e^x{\sec }^2(e^x)\end{array}$