Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 141: 40


$$A'(v)=\frac{1}{3}\bigg(16v^{5/3}+2v^{-1/3}+4v^{-7/3} \bigg)$$

Work Step by Step

$A(v)=v^{2/3}(2v^2+1-v^{-2})=2v^{8/3}+v^{2/3}-v^{-4/3}$ Differentiating with respect to $v$, using power rule, $$A'(v)=2\bigg(\frac{8}{3}\bigg)v^{8/3-1}+\frac{2}{3}v^{2/3-1}+\frac{4}{3}v^{-4/3-1}$$ $$A'(v)=\frac{16}{3}v^{5/3}+\frac{2}{3}v^{-1/3}+\frac{4}{3}v^{-7/3}=\frac{1}{3}\bigg(16v^{5/3}+2v^{-1/3}+4v^{-7/3} \bigg)$$
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