Chapter 7.2, Problem 7QR

To determine

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

Answer to Problem 7QR

  $\text{The required solution is, }\frac{dy}{dx}=-\tan x$

Explanation of Solution

Given information: $\text{The equation is},y=\ln \cos x.$

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

  $\begin{array}{l}\text{Find the derivative using chain rule,}\\ y=\ln \cos x\\ \frac{dy}{dx}=\frac{1}{\cos x}\text{.}\frac{d}{dx}\left(\cos x\right)\\ =\frac{1}{\cos x}\text{.}-\sin x\\ =\frac{-\sin x}{\cos x}\\ =-\tan x\\ \text{Hence, the required solution is, }\frac{dy}{dx}=-\tan x.\end{array}$