Question

Derivata f(x) =x+1/x-1

Answer 1

$f'(x)=\left(\dfrac{x+1}{x-1}\right)^{'}=\dfrac{(x+1)'\cdot (x-1)-(x-1)'\cdot (x+1)}{(x-1)^2} = \\ =\dfrac{x-1-x-1}{(x-1)^2}=\boxed{-\dfrac{2}{(x-1)^2}}$