Find if the function differentiable $$f(x,y)=\begin{cases} \dfrac{x^2-y^2}{\sqrt{x^2+y^2}}, (x,y)\neq (0,0)\\ 0, (x,y)=(0,0)\\ \end{cases}$$
Looking at
$\dfrac{\partial f}{\partial x}(0,0)=\lim_{\Delta x\to 0}\frac{\Delta x}{|\Delta x|}$
$\dfrac{\partial f}{\partial y}(0,0)=\lim_{\Delta y\to 0}\frac{-\Delta y}{|\Delta y|}$
Which both has no limit and therefore no partial derivative, if just one partial derivative was not defined, is it enough to say that the function is not differentiable