University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 3 - Section 3.11 - Linearization and Differentials - Exercises - Page 199: 26



Work Step by Step

We evaluate the function: $y=\cos({{x}^2})$ on differentiating the above: $\frac{dy}{dx}=\frac{d\cos({{x}^2})}{dx}$ or $\frac{dy}{dx}=-\sin({{x}^2})\frac{d({x})^2}{dx}$ or $\frac{dy}{dx}={-2{x}}\sin({{x}^2})$ or ${dy}={-2{x}}\sin({{x}^2}){dx}$ The final answer is: ${dy}={-2{x}}\sin({{x}^2}){dx}$
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