Differentiation

$y\left[\frac{x \sin x}{\log \cos x}+\log (\log \sin x)+\frac{1}{\log x}-\log (\log x)\right]$

$y\left[\frac{x \cos x}{\log \sin x}-\log (\log \sin x)+\frac{1}{\log x}+\log (\log x)\right]$

$y\left[\frac{x \cot x}{\log \sin x}+\log (\log \sin x)-\frac{1}{\log x}-\log (\log x)\right]$

$y\left[\frac{x \cot x}{\log \sin x}-\log (\log \sin x)+\frac{1}{\log x}-(\log x)\right]$