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: 57

Answer

$f'(\theta)=\dfrac{\sin{4\theta}}{2}.$

Work Step by Step

$u=\sin{2\theta}$; $\dfrac{du}{d\theta}=2\cos{2\theta}.$ $\dfrac{d}{du}f(u)=\dfrac{u}{2}.$ $\dfrac{d}{d\theta}f(\theta)=\dfrac{d}{du}f(u)\times\dfrac{du}{d\theta}=(2\cos{2\theta})(\dfrac{\sin{2\theta}}{2})$ $=\cos{2\theta}\sin{2\theta}=\dfrac{\sin{4\theta}}{2}.$
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