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