[m]\frac{ ∂z }{ ∂x }=z`_{x}=(\frac{xy}{x-y})`_{x}=\frac{(xy)`_{x}\cdot (x-y)-(xy)\cdot (x-y)`_{x}}{(x-y)^2}=\frac{y\cdot (x-y)-xy}{(x-y)^2}=\frac{yx-y^2-xy}{(x-y)^2}=-\frac{y^2}{(x-y)^2}[/m]
[m]\frac{ ∂z }{ ∂y }=z`_{y}=(\frac{xy}{x-y})`_{y}=\frac{x\cdot (x-y)-(xy)\cdot (-1)}{(x-y)^2}=\frac{x^2-xy+xy}{(x-y)^2}=\frac{x^2}{(x-y)^2}[/m]