Answer
$y^{\prime}=\frac{3(\ln x)^2}{x}$
Work Step by Step
$y=(\ln x)^3$
We differentiate both sides to obtain:
$y^{\prime}=3(\ln x)^{3-1}\frac{d}{dx}(lnx)$
$y^{\prime}=3(\ln x)^2\frac{1}{x}$
$y^{\prime}=\frac{3(\ln x)^2}{x}$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 3 - Section 3.8 - Derivatives of Inverse Functions and Logarithms - Exercises - Page 175: 20
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