Calculus 8th Edition

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

Chapter 2 - Derivatives - Review - Exercises - Page 197: 38


$\dfrac {4x-10}{\left( x-2\right) \left( x-3\right) }$

Work Step by Step

$y=\dfrac {\left( x-1\right) \left( x-4\right) }{\left( x-2\right) \left( x-3\right) }=\dfrac {x^{2}-5x+4}{\left( x^{2}-5x+6\right) }=1-\dfrac {2}{x^{2}-5x+6}\Rightarrow \dfrac {dy}{dx}=2\dfrac {\dfrac {d}{dx}\left( x^{2}-5x+6\right) }{\left( x^{2}-5x+6\right) ^{2}}=\dfrac {2\left( 2x-5\right) }{x^{2}-5x+6}=\dfrac {4x-10}{\left( x-2\right) \left( x-3\right) }$
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