Question

Find the derivative of $\log \left(\sin \right(\log x\left)\right)$.

Answer 1

Let $p=log\left[\sin \right(logx\left)\right]$

Differentiating P wrt x we have

$\frac{dp}{dx}=\frac{d}{dx}\left[log\right(\sin \left(logx\right)\left)\right]$

$\frac{dp}{dx}=\frac{1}{\sin \left(logx\right)}\cdot \cos \left(logx\right)\times \frac{1}{x}$

$[\frac{dp}{dx}=\frac{\cot \left(logx\right)}{x}]$.