Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 386: 26


$$ f'(x)= \sin (2x) e^{\sin^2 x}.$$

Work Step by Step

Recall that $(e^x)'=e^x$ Recall that $(\sin x)'=\cos x$. Recall that $2\sin x \cos x=\sin 2x$ Since $ f(x)=e^{\sin^2 x}$, then the derivative, using the chain rule, is given by $$ f'(x)=e^{\sin^2 x} (\sin^2 x)'=(2\sin x\cos x)e^{\sin^2 x}=\sin (2x) e^{\sin^2 x}.$$
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