Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - Chapter Review Exercises - Page 164: 64


$$ y''= \frac{14}{25}x^{-12/5}.$$

Work Step by Step

Recall that $(x^n)'=nx^{n-1}$ Given $ y=x^{-2/5}$, then by using the power rule, we have $$ y'=-\frac{2}{5}x^{-7/5},$$ and the second derivative $ y''$ is given by $$ y''=-\frac{2}{5}(-\frac{7}{5})x^{-12/5}=\frac{14}{25}x^{-12/5}.$$
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