University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.9 - Inverse Trigonometric Functions - Exercises - Page 181: 21


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

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