calculus - Showing that the function given by $f(x,y)=frac{xy}{sqrt{x^2+y^2}}$ and $f(0,0)=0$ is continuous but not differentiable

Let
$$f(x,y) = \begin{cases} \dfrac{xy}{\sqrt{x^2+y^2}} & \text{if $(x,y)\neq(0,0)$ } \\[2ex] 0 & \text{if $(x,y)=(0,0)$ } \\ \end{cases}$$
Show that this function is continuous but not differentiable at $(0,0),$ although it has both partial derivatives existing there.

I can show this function is continous and the partial derivatives exist. But how can I show that this function is not differentiable?

Is showing that the function is differentiable similar to showing that a derivative exists?