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: 31


$\frac{2}{x} \ln x$

Work Step by Step

$y= (\ln x)^{2}$ Let us substitute $t= \ln x$ Then, $y= t^{2}$ According to the chain rule, $\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}= 2t\times\frac{1}{x}$ Undoing substitution, we obtain $\frac{dy}{dx}= \frac{2}{x} \ln x$
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