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