Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.4 Exercises: 56

Answer

$g'(\theta)=-8\sin{16\theta}.$

Work Step by Step

$u=\cos{8\theta}$; $\dfrac{du}{d\theta}=-8\sin{8\theta}$ $\dfrac{d}{du}g(u)=2u$ $\dfrac{d}{d\theta}g(\theta)=\dfrac{d}{du}g(u)\times\dfrac{du}{d\theta}=(2cos{8\theta})(-8\sin{8\theta})$ $=-16\cos{8\theta}\sin{8\theta}$ $=-8\sin{16\theta}.$
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