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: 21


$(\ln t)^2+2\ln t$

Work Step by Step

$y=t(\ln t)^2$ We differentiate both sides to obtain: $y^{\prime}=t(\ln t)^2{\prime}+(\ln t)^2(t)^{\prime}$ $y^{\prime}=t(2\ln t)(\ln t)^{\prime}+(\ln t)^2(1)$ $y^{\prime}=t(2\ln t)(\frac{1}{t})+(\ln t)^2$ $y^{\prime}=(\ln t)^2+2\ln t$
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