Question

Let $y={\sin }^{-1}\left(\cos x\right)$ then find $\frac{dy}{dx}$.

Answer 1

Given, $y={\sin }^{-1}\left(\cos x\right)$

or,$y={\sin }^{-1}\sin (\frac{\pi }{2}-x)$

or, $y=\frac{\pi }{2}-x$.

Now differentiating both sides with respect to $x$ we get,

$\frac{dy}{dx}=-1$.