Question

Diff w.r.t $X$
${\cos }^{-1}(1-2{\sin }^{2}x)$

Answer 1

We have

${\cos }^{-1}(1-2{\sin }^{2}x)$

Suppose that

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

$y={\cos }^{-1}\cos 2x[\therefore \cos 2x=1-2{\sin }^{2}x]$

$y=2x$

differentiation this w.r.t and we get

$\frac{dy}{dx}=\frac{d}{dx}\left(2x\right)$

$=2\frac{dx}{dx}$

$=\frac{dy}{dx}=2$

Hence, this is the answer.