Answer
$g'(x)=\frac{1-2x}{x}$
Work Step by Step
Use the derivative of natural log and apply the chain rule:
$g'(x)=\frac{1}{xe^{-2x}}\times(-2xe^{-2x}+e^{-2x})$
After simplifying:
$g'(x)=\frac{1-2x}{x}$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 3 - Section 3.6 - Derivatives of Logarithmic Functions - 3.6 Exercises - Page 223: 9
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