$$ y'= e^x sech^2 e^x .$$
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 $$ y'=sech^2 e^x (e^x)'=e^x sech^2 e^x .$$
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