Question

Производная f(x)=4/x-1 +x на отрезке [-2;0]

Answer 1

$f(x)= frac{4}{x-1}+x$
$x neq 1$
$f'(x)=frac{-1}{(x-1)^{2}}+1=frac{-1+(x-1)^{2}}{(x-1)^{2}}=frac{-1+x^{2}-2x+1}{(x-1)^{2}}=frac{x^{2}-2x}{(x-1)^{2}}=frac{x(x-2)}{(x-1)^{2}}$