Answer
$\frac{3}{x(x+3)}$
Work Step by Step
$f(x)=ln(\frac{2x}{x+3})$
$=ln(2x)-ln(x+3)$
$=ln2+ln x-ln(x+3)$
$f'(x)=0+\frac{1}{x}-\frac{1}{x+3}$
$=\frac{x+3-x}{x(x+3)}$
$=\frac{3}{x(x+3)}$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.1 Exercises - Page 325: 52
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