Question

Differentiate the following w.r.t.x:
${\sin }^{-1}x+{\cos }^{-1}x$

Answer 1

Let $y={\sin }^{-1}x+{\cos }^{-1}x$

We know, ${\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}$

Therefore, $y=\frac{\pi }{2}$

Hence,

$\frac{dy}{dx}=0$