# How do you use the quotient rule to find the derivative of y=x/(x-1)^2 ?

Sep 21, 2014

By Quotient Rule,

$y ' = \frac{1 \cdot {\left(x - 1\right)}^{2} - x \cdot 2 \left(x - 1\right)}{{\left[{\left(x - 1\right)}^{2}\right]}^{2}}$

by factoring out $\left(x - 1\right)$ from the numerator,

$= \frac{\left(x - 1\right) \left(x - 1 - 2 x\right)}{{\left(x - 1\right)}^{4}}$

by cancelling out $\left(x - 1\right)$,

$= \frac{- x - 1}{{\left(x - 1\right)}^{3}}$

by factoring out $- 1$ from the numerator,

$= - \frac{x + 1}{{\left(x - 1\right)}^{3}}$