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: 21

Answer

$-\frac{1}{x}$

Work Step by Step

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