Question

Differentiate

sin (log sin x)

Answer 1

$$\begin{gathered} \mathrm{Let}y=\sin \left(\log \sin x\right) \\ \mathrm{Differentiate}\mathrm{it}\mathrm{with}\mathrm{respect}\mathrm{to}x\mathrm{we}\mathrm{get}, \\ \frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}=\frac{d}{dx}\sin \left(\log \sin x\right) \\ =\cos \left(\log \sin x\right)\frac{d}{dx}\left(\log \sin x\right)\left[\mathrm{Using}\mathrm{chain}\mathrm{rule}\right] \\ =\cos \left(\log \sin x\right)\times \frac{1}{\sin x}\frac{d}{dx}\sin x\left[\mathrm{Using}\mathrm{chain}\mathrm{rule}\right] \\ =\cos \left(\log \sin x\right)\frac{\cos x}{\sin x} \\ =\cos \left(\log \sin x\right)\cot x \\ \mathrm{Hence},\frac{d}{dx}\sin \left(\log \sin x\right)=\cos \left(\log \sin x\right)\cot x \end{gathered}$$