Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises: 34

Answer

$\frac{e^x}{(1-e^x)^2}$

Work Step by Step

$\frac{d}{dx} \frac{e^x}{1-e^x}$ $=\frac{(1-e^x)\frac{d}{dx}(e^x)-e^x\frac{d}{dx}(1-e^x)}{(1-e^x)^2}$ $=\frac{(1-e^x)e^x-e^x(-e^x)}{(1-e^x)^2}$ $=\frac{e^x-e^{2x}+e^{2x}}{(1-e^x)^2}$ $=\frac{e^x}{(1-e^x)^2}$
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