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: 55

Answer

$f'(\theta)=10\tan{5\theta}\sec^2{5\theta}.$

Work Step by Step

$u=\tan{5\theta}$; $\dfrac{du}{d\theta}=5\times\sec^2{5\theta}=5\sec^2{5\theta}.$ $\dfrac{d}{du}f(u)=2u$ $\dfrac{d}{d\theta}f(\theta)=\dfrac{d}{du}f(u)\times\dfrac{du}{d\theta}=2\tan{5\theta}\times5\sec^2{5\theta}=10\tan{5\theta}\sec^2{5\theta}.$
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