Question

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

Answer 1

Let $y={\sin }^{-1}(x^2-1)$

Differentiating w.r.t. x,

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

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