Answer
$\frac{5}{x}$
Work Step by Step
$y= \ln (x^{5})$
Put $t= x^{5}$
Then, $y=\ln t$
According to the chain rule,
$\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}=\frac{1}{t}\times5x^{4}$
$=\frac{5x^{4}}{x^{5}}=\frac{5}{x}$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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