Question

find the derivative of (x^2+2x-2)/(x62-2x+2)

Answer 1

$y=(x^2+2x-2)/(x^2-2x+2)\\\\ y=1+\frac{4x-4}{x^2-2x+2}=1+\frac{u}{v}\\\\\frac{dy}{dx}=y'=\frac{vu'-uv'}{v^2}\\\\=\frac{(x^2-2x+2)4-4(x-1)(2x-2)}{(x^2-2x+2)^2}$

$=4*\frac{x^2-2x+2-(2x^2-4x+2)}{(x^2-2x+2)^2}\\\\=4*\frac{2x-x^2}{(x^2-2x+2)^2}=\frac{4x(2-x)}{(x^2-2x+2)^2}$