Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 42


$$ y'= \frac{3}{x\ln x}.$$

Work Step by Step

Recall that $(\ln x)'=\dfrac{1}{x}$ Since $ y=\ln (\ln x)^3$, first we simplify $ y $ as follows $$ y=3\ln (\ln x)$$ then by the chain rule, we have $$ y'=3\frac{1/x}{\ln x}=\frac{3}{x\ln x}.$$
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