## Calculus (3rd Edition)

Published by W. H. Freeman

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

#### Answer

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

#### 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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