I am trying to proof that if $f$ is two times differentiable then exists limit

$$

lim_{(x,y)to(x_0,y_0)}frac{f(x,y)-f(x_0,y)-f(x,y_0)+f(x_0,y_0)}{(x-x_0)(y-y_0)}

$$

I have been thinking that idea is add and subtract by conveniently but I don’t have idea. Some hint?