Question

Differentiate the following w.r.t.x:
${\cos }^{-1}\left(\sin x^2\right)$

Answer 1

$y={\cos }^{-1}\left(\sin x^2\right)$

Differentiating w.r.t. x,

$\frac{dy}{dx}=-\frac{1}{\sqrt{1-(\sin x^2{)}^2}}\left(\cos x^2\right)\left(2x\right)$