Question

Differentiate \[\log \left( \cos x^2 \right)\] ?

Answer 1

\[\text{Let } y = \log \left( \cos x^2 \right)\]

Differentiating with respect to x,

\[\frac{d y}{d x} = \frac{d}{dx}\left\{ \log\left( \cos x^2 \right) \right\}\]

\[ = \frac{- 2x \sin x^2}{\cos x^2} \]

\[ = - 2x \tan x^2 \]

\[So, \frac{d}{dx}\left\{ \log\left( \cos x^2 \right) \right\} = - 2x \tan x^2\]