Question

Find the derivative of $\frac{x}{(x-1)}$

Answer 1

Given expression

$y=\frac{x}{x-1}$

$\frac{dy}{dx}=\frac{d}{dx}\frac{x}{x-1}$

By using ${\left(\frac{u}{v}\right)}^{\prime }=\frac{v{u}^{\prime }-u{v}^{\prime }}{v^2}$

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

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