Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.4 - The Chain Rule - 3.4 Exercises: 12

Answer

$g'(\theta)=-2\sin\theta\cos\theta$ or $g'(\theta)=-\sin2\theta$

Work Step by Step

$g(\theta)=\cos^{2}\theta$ Differentiate using the chain rule: $g'(\theta)=2\cos\theta(\cos\theta)'=2(\cos\theta)(-\sin\theta)=...$ $...=-2\sin\theta\cos\theta$ Also you can use the identity $2\sin\theta\cos\theta=\sin(2\theta)$ to present the answer like this: $g'(\theta)=-\sin2\theta$
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