f(x)=(3x²-4x)/(2(x-1)²)
( 3x²-4x)´=6x-4
( 2(x-1)²)´=2*2(x-1)=4(x-1)
f´(x)=[(6x-4)(2(x-1)^2)-(4(x-1))(3x²-4x)]/(2(x-1)²
) ^2
=[(6x-4)(2*(x-1)(x-1))-(4*(x-1))(3x²-4x)]/(2(x-1)(
x-1)) ^2
=[(x-1)(6x-4)(x-1)*2-4*(3x^2-4x)]/[(2(x-1)(x-1)*2*
(x-1)(x-1)]
on simplifie
=[(6x^2-6x-4x+4)*2-12x^2+16x]/[(2(x-1)*2*(x-1)(x-1
)]
=[12x^2-12x-8x+8-12x^2+16x]/(2*2*(x-1)^3)
=(-4x+8)/(2*2*(x-1)^3)
on simplifie
=(-x+2)/(x-1)^3