Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.3 Introduction To Techniques Of Differentiation - Exercises Set 2.3: 14

Answer

$f'(x)=\sqrt[3] {-\frac{8}{27x^{4}}}$

Work Step by Step

$f(x)=\sqrt[3] \frac{8}{x}=2x^{-\frac{1}{3}}$ $f'(x)=2(-\frac{1}{3})x^{-\frac{1}{3}-1}$ $f'(x)=-\frac{2}{3}x^{-\frac{4}{3}}$ $f'(x)=-\frac{2}{3\sqrt[3] {x^{4}}}$ $f'(x)=\sqrt[3] {-\frac{8}{27x^{4}}}$
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