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: 25


$$ f'(x)=(1+\frac{1}{x})e^{x+\ln x}.$$

Work Step by Step

Recall that $(e^x)'=e^x$ Recall that $(\ln x)'=\dfrac{1}{x}$ Since $ f(x)=e^{x+\ln x}$, then the derivative, using the chain rule, is given by $$ f'(x)=e^{x+\ln x} (x+\ln x)'=(1+\frac{1}{x})e^{x+\ln x}.$$
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