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: 52


$$ y'= -\sin( \theta)\sin(\cos \theta) \sin(\cos(\cos \theta)).$$

Work Step by Step

Recall that $(\cos x)'=-\sin x$. Since $ y=\cos(\cos(\cos \theta ))$, then by the chain rule, the derivative $ y'$ is given by $$ y'= -\sin(\cos(\cos \theta))(-\sin(\cos \theta))(-\sin \theta)\\= -\sin( \theta)\sin(\cos \theta) \sin(\cos(\cos \theta)).$$
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