Chapter 7.3, Problem 4QR

To determine

  $\text{ To find }\frac{dy}{dx}\text{.}$

Answer to Problem 4QR

  $\text{The required solution is, }\frac{dy}{dx}=\frac{1}{\sqrt{1-{\left(x+3\right)}^2}}.$

Explanation of Solution

Given information: $\text{The equation is},y={\sin }^{-1}\left(x+3\right)$

Calculation : $\frac{dy}{dx}\text{ is obtained as,}$

  $\begin{array}{l}y={\sin }^{-1}\left(x+3\right)\\ \frac{dy}{dx}=\frac{1}{\sqrt{1-{\left(x+3\right)}^2}}\left(\frac{d}{dy}\left({\sin }^{-1}\right)=\frac{1}{\sqrt{1-u^2}}\text{, where }u=x+3.\right)\\ \\ \text{Hence, the required solution is, }\frac{dy}{dx}=\frac{1}{\sqrt{1-{\left(x+3\right)}^2}}.\end{array}$