Answer
$-(\frac{2x}{\sqrt (1-x^4)})$
Work Step by Step
It is given $y$ = $cos^{-1}(x^{2})$
so $ \frac{dy}{dx}$ =$\frac{d(cos^{-1}(x^{2}))}{dx}$
let $u$ = $(x^{2})$
on applying chain rule
$\frac{d(cos^{-1}(u))}{dx}$ = $-(\frac{1}{\sqrt (1-u^{2})})$$\times$ $\frac{du}{dx}$
or $\frac{dy}{dx}$ = $-(\frac{1}{\sqrt (1-(x^{2})^2)})$$\times$ $2x$
or $\frac{dy}{dx}$ = $-(\frac{2x}{\sqrt (1-x^4)})$
Hence. the final answer is: $-(\frac{2x}{\sqrt (1-x^4)})$
