Answer
$-\dfrac {1}{\left( x-1\right) ^{2}}$
Work Step by Step
$\dfrac {d}{dx}\left( 1-x^{-1}\right) ^{-1}=-1\times \left( 1-x^{-1}\right) ^{1-1}\times \left( \dfrac {d}{dx}\left( 1-x^{-1}\right) \right) =-\dfrac {1}{\left( 1-\dfrac {1}{x}\right) ^{2}\times x^{2}}=-\dfrac {1}{\left( x-1\right) ^{2}}$
