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: 16


$$ y'= \frac{1+e^x}{x+e^x}.$$

Work Step by Step

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