Calculus 10th Edition

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: 58

Answer

$\frac{2}{3(x-1)(x+1)}$

Work Step by Step

$y=ln \sqrt[3] \frac{x-1}{x+1}$ $=ln (\frac{x-1}{x+1})^{1/3}$ $=\frac{1}{3}ln(\frac{x-1}{x+1})$ $=\frac{1}{3}(ln(x-1)-ln(x+1))$ $=\frac{1}{3}(\frac{1}{x-1}-\frac{1}{x+1})$ $=\frac{1}{3}(\frac{x+1-x+1}{(x-1)(x+1)})$ $=\frac{2}{3(x-1)(x+1)}$
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