Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 20


$$ y'= 3\cosh^2x \sinh x \cosh( \cosh^3 x) .$$

Work Step by Step

Recall that $(\sinh x)'=\cosh x$ Recall that $(\cosh x)'=\sinh x$ Since $ y=\sinh (\cosh^3 x)$, then the derivative, by using the chain rule, is given by $$ y'=\cosh( \cosh^3 x) ( \cosh^3 x)'=3\cosh^2x \sinh x \cosh( \cosh^3 x) .$$
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