Differentiability of a two variable function $f(x,y)=\dfrac{1}{1+x-y}$ We're given the following function :
$$f(x,y)=\dfrac{1}{1+x-y}$$
Now , how to prove that the given function is differentiable at $(0,0)$ ?
I found out the partial derivatives as $f_x(0,0)=(-1)$ and $f_y(0,0)=1$ ,
Clearly the partial derivatives are continuous , but that doesn't guarantee differentiability , does it ?
Is there any other way to prove the same ?

If all partial derivatives of a function (over all possible variables) are continuous at some point, then the function is differentiable at that point.
