Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - Chapter Review Exercises - Page 164: 50


$-\sin x \sec^{2}(\cos x)$

Work Step by Step

$y= \tan(\cos x)$ Let $\cos x= t$ Then, $y= \tan t$. According to the chain rule, $\frac{dy}{dx}= \frac{dy}{dt}\cdot\frac{dt}{dx}$ Therefore, $\frac{dy}{dx}=\sec^{2}t\times-\sin x$ $=-\sin x \sec^{2}(\cos x)$
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