Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Review - Exercises: 16

Answer

$4\dfrac {\left( 2\left( u+1\right) -u^{2}\right) \left( u-1\right) ^{3}}{\left( u^{2}+u+1\right) ^{5}}$

Work Step by Step

$\dfrac {d}{dx}\left( \dfrac {u-1}{u^{2}+u+1}\right) ^{4}=4\times \left( \dfrac {u-1}{u^{2}+u+1}\right) ^{3}\times \dfrac {d}{dx}\left( \dfrac {u-1}{u^{2}+u+1}\right) =4\left( \dfrac {u-1}{u^{2}+u+1}\right) ^{3}\times \dfrac {1\times \left( u^{2}+u+1\right) -\left( 2u+1\right) \left( u-1\right) }{\left( u^{2}+u+1\right) 2}=4\dfrac {\left( 2\left( u+1\right) -u^{2}\right) \left( u-1\right) ^{3}}{\left( u^{2}+u+1\right) ^{5}}$
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