Question

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

Answer 1

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

Differentiating with respect to x,

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

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

\[ = - \sin \left( \log x \right)^2 \frac{2\log x}{x} \]

\[ = \frac{- 2\log x \sin \left( \log x \right)^2}{x}\]

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