Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Review - Exercises: 39

Answer

$y'=2[\tan(\sin\theta)][\sec^{2}(\sin\theta)]\cos\theta$

Work Step by Step

$y=\tan^{2}(\sin\theta)$ Start the differentiation process by using the chain rule: $y'=2[\tan(\sin\theta)][\tan(\sin\theta)]'=...$ Apply the chain rule one more time to evaluate the indicated derivative: $...=2[\tan(\sin\theta)][\sec^{2}(\sin\theta)](\sin\theta)'=...$ Evaluate the remaining derivative and simplify: $...=2[\tan(\sin\theta)][\sec^{2}(\sin\theta)]\cos\theta$
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