Calculus 8th Edition

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

Chapter 2 - Derivatives - Review - Exercises - Page 197: 18


$\sqrt {7}\left( x+\dfrac {1}{x^{2}}\right) ^{\sqrt {7}-1}\left( 1-\dfrac {2}{x^{3}}\right) $

Work Step by Step

$y=\left( x+\dfrac {1}{x^{2}}\right) ^{\sqrt {7}}=y'=\sqrt {7}\times \left( x+x^{-2}\right) ^{\sqrt {7}-1}\times \left( \dfrac {d}{dx}\left( x+x^{-2}\right) \right) =\sqrt {7}\left( x+\dfrac {1}{x^{2}}\right) ^{\sqrt {7}-1}\left( 1-\dfrac {2}{x^{3}}\right) $
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