Question

If $y=f\left(\sin x\right)$ and $f^{\prime }\left(x\right)={\sin }^{-1}x$ then $\frac{dy}{dx}$ is-

Answer 1

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

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

$=f^{\prime }\left(\sin x\right).\frac{d}{dx}\left(\sin x\right)$

$=f^{\prime }\left(x\right).\cos x$

Given : $f^{\prime }\left(x\right)={\sin }^{-1}x$

$\therefore f^{\prime }\left(\sin x\right)={\sin }^{-1}\sin x=x$

$\therefore \frac{dy}{dx}=x\cos x$