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Question
Differentiate \[\log \left( \cos x^2 \right)\] ?
Solution
\[\text{Let } y = \log \left( \cos x^2 \right)\]
Differentiating with respect to x,
\[\frac{d y}{d x} = \frac{d}{dx}\left\{ \log\left( \cos x^2 \right) \right\}\]
\[ = \frac{- 2x \sin x^2}{\cos x^2} \]
\[ = - 2x \tan x^2 \]
\[So, \frac{d}{dx}\left\{ \log\left( \cos x^2 \right) \right\} = - 2x \tan x^2\]
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