Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - Review Exercises: 48

Answer

$f''(x)=-\dfrac{16}{5x\sqrt[5]{x^4}}.$

Work Step by Step

$f(x)=20x^{\frac{1}{5}}$ Using the Power Rule: $f'(x)=(\frac{1}{5})(20)(x^{\frac{1}{5}-1})=\dfrac{4}{\sqrt[5]{x^4}}.$ Using the Power Rule: $f''(x)=(-\frac{4}{5})(4)x^{-\frac{4}{5}-1}=-\dfrac{16}{5x\sqrt[5]{x^9}}.$
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