Calculus 10th Edition

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

Chapter 2 - Differentiation - Review Exercises: 49

Answer

$f''(\theta)=6\sec^2{\theta}\tan{\theta}.$

Work Step by Step

Using the Power Rule: $f'(\theta)=3\sec^2{\theta}.$ Using the Chain Rule with $u=\sec{\theta}\rightarrow\dfrac{du}{dx}=\sec{\theta}\tan{\theta}$ $f(u)=3u^2\rightarrow f'(u)=6u$ $f''(\theta)=6(\sec{\theta})(\sec{\theta}\tan{\theta})=6\sec^2{\theta}\tan{\theta}$
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