Question

Find the derivative of $y=\sin \left(\sin \right(\sin x\left)\right)$

Answer 1

$y=\sin \left(\sin \right(\sin x\left)\right)$

$\Rightarrow$ Applying chain Rule here

$\Rightarrow \frac{dy}{dx}=\frac{d}{dx}\sin \left(\sin \right(\sin x\left)\right)\frac{d}{dx}\sin \left(\sin x\right)\cdot \frac{d}{dx}\left(\sin x\right)$

$=\cos \left(\sin \right(\sin x\left)\right)\cos \left(\sin x\right)\cos x$

$=\cos \left(\sin \right(\sin x\left)\right)\cdot \cos \left(\sin x\right)\cdot \cos x$.