Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.2* The Natural Logarithmic Functions - 6.2* Exercises: 25

Answer

$-\frac{2a}{a^2-x^2}$

Work Step by Step

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