Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4 Derivatives of Logarithmic Functions - 6.4 Exercises: 6

Answer

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

Work Step by Step

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