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: 32



Work Step by Step

$y= \ln (x^{5})$ Put $t= x^{5}$ Then, $y=\ln t$ According to the chain rule, $\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}=\frac{1}{t}\times5x^{4}$ $=\frac{5x^{4}}{x^{5}}=\frac{5}{x}$
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