## University Calculus: Early Transcendentals (3rd Edition)

$-(\frac{2x}{\sqrt (1-x^4)})$
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: $-(\frac{2x}{\sqrt (1-x^4)})$