University Calculus: Early Transcendentals (3rd Edition)

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


$y^{\prime}=\frac{3(\ln x)^2}{x}$

Work Step by Step

$y=(\ln x)^3$ We differentiate both sides to obtain: $y^{\prime}=3(\ln x)^{3-1}\frac{d}{dx}(lnx)$ $y^{\prime}=3(\ln x)^2\frac{1}{x}$ $y^{\prime}=\frac{3(\ln x)^2}{x}$
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