Chapter 5.6, Problem 5QR

To determine

To find: the value of $\frac{dy}{dx}$ .

Answer to Problem 5QR

The value of $\frac{dy}{dx}$ is

  $2x\cos y^2$ .

Explanation of Solution

Given information:

Given data:

  $x^2=\tan y$

Calculation :

To calculate the value of $\frac{dy}{dx}$ ,

Therefore,

  $x^2=\tan y$

We have to differentiate using product rule.

  $\begin{array}{l}2xdx={\text{sec}}^{2}ydy\\ \frac{dy}{dx}=\frac{2x}{{\text{sec}}^{2}y}\\ \frac{dy}{dx}=2x{\text{cos}}^{2}y\left[\text{Since }\frac{1}{{\text{sec}}^{2}y}={\text{cos}}^{2}y\right]\end{array}$

Hence, the value of $\frac{dy}{dx}$ is $2x\cos y^2$ .