Answer
$-\frac{1}{x(\ln x)^2}$
Work Step by Step
$\frac{d}{dx}\frac{1}{\ln x}$
$=\frac{d}{dx}(\ln x)^{-1}$
$=-(\ln x)^{-2}\frac{d}{dx}\ln x$
$=-\frac{1}{(\ln x)^2}*\frac{1}{x}$
$=-\frac{1}{x(\ln x)^2}$
Calculus 8th Edition
by Stewart, James
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 - Page 436: 6
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