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: 14


$$ y'=\cosh x\tanh x+\sinh x\, sech^2 x .$$

Work Step by Step

Since $ y=\sinh x\tanh x $, then the derivative $ y'$, using the product rule $(uv)'=uv'+u'v $ and the facts that $(\sinh x)'=\cosh x $ and $(\tanh x)'=sech^2x $, is given by $$ y'=\cosh x\tanh x+\sinh x\, sech^2 x .$$
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