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: 44


$$ y'=\frac{1}{x+1}- \frac{3x^2}{x^3+1}.$$

Work Step by Step

Since $ y=\ln\left( \frac{x+1}{x^3+1}\right)$, first we simplify $ y $ as follows $$ y=\ln (x+1)- \ln (x^3+1)$$ then we have $$ y'=\frac{1}{x+1}- \frac{3x^2}{x^3+1}.$$
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