Производная функции f(x)=(x^3-3x^2+3x-1)/(x-1)

Question

Производная функции f(x)=(x^3-3x^2+3x-1)/(x-1)

Answer 1

F' = [(3x^2 -3*2*x+3)*(x-1) - (x^3-3x^2+3x-1)*1]/(x-1)^2 = 
=(3x^3-6x^2+3x-3x^2+6x-3 -x^3+3x^2-3x+1)/(x-1)^2 = (2x^3 -6x^2+6x-4)/(x-1)^2 =
=2(x^3-3x^2+3x-2)/(x-1)^2