Differentiation — Maths STD 12 Science — Question

$y=\cos ^{-1}\left(2 x \sqrt{1-x^2}\right)$
put $x=\sin \theta$
$\theta=\sin ^{-1} x$
$=\cos ^{-1}\left(2 \sin \theta \sqrt{1-\sin ^2 \theta}\right)$
$=\cos ^{-1}(\sin 2 \theta)$
$=\cos ^{-1}\left(\cos \left(\frac{\pi}{2}-2 \theta\right)\right)$
$y=\frac{\pi}{2}-2 \theta=\frac{\pi}{2}-2 \sin ^{-1} x$
Differentiating with respect to 'x', we get
$\frac{d y}{d x}=0-\frac{2}{\sqrt{1-x^2}}=\frac{-2}{\sqrt{1-x^2}}$