Answer
$$ y'= e^x sech^2 e^x .$$
Work Step by Step
Recall that $(\tanh x)'=\sec^2 x$
Recall that $(e^x)'=e^x$
Since $ y=\tanh e^x $, then the derivative, by using the chain rule, is given by
$$ y'=sech^2 e^x (e^x)'=e^x sech^2 e^x .$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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: 19
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