Chapter 4.1, Problem 24E

To determine

To calculate:The differentiation of the given function.

Answer to Problem 24E

The differentiation is $\frac{5\times {\sec }^{2}5x}{2\times \sqrt{\tan 5x}}$ .

Explanation of Solution

Given information: Given function is $y=\sqrt{\tan 5x}$ .

Formula used: $\frac{d(x^n)}{dx}=n{x}^{n-1}\text{and}\frac{d(\tan x)}{dx}={\sec }^{2}x$ with chain rule.

Calculation:

  $y=\sqrt{\tan 5x}$

Differentiate with respect to x ,

  $\begin{array}{l}\frac{dy}{dx}=\frac{d(\sqrt{\tan 5x)}}{d(\tan 5x)}\times \frac{d(\tan 5x)}{d(5x)}\times \frac{d(5x)}{dx}\\ \frac{dy}{dx}=\frac{1}{2\times \sqrt{\tan 5x}}\times {\sec }^{2}5x(5)\\ \frac{dy}{dx}=\frac{5\times {\sec }^{2}5x}{2\times \sqrt{\tan 5x}}\end{array}$