I am trying to find the derivative of $y= (1-x^{-1})^{-1}$ to make it simple I use the chain rule and
$u = 1-x^{-1}$
$y = u^{-1}$
$y' = -1u^{-2}u' = -1(1-x^{-1})^{-2}(x^{-2})$
The problem is that this is not what my book gets and I am wondering if there is some strange power rule I overlooked or some other way to do this problem that gives me a different answer, or maybe I just need to factor is out somehow.