multivariable calculus - Prove the function is not differentiable at (0,0)

Take the function

$$\begin{cases}f(x,y)=(x^2+y^2)/\sin(\sqrt{x^2+y^2}) & \text{when } 0<\lvert (x,y)\rvert<\pi\\ 0 & \text{when } (x,y)=(0,0) \end{cases}$$

I got that this function is differentiable at $(0,0)$. I calculated the partial derivatives at $(0,0)$ of which both were $0$ and trying to show the definition of differentiability is not satisfied but I keep getting that it is. Plz help.

Answer

Calculating the partial derivatives at $(0,0)$ you get a limit of the form:

$$\lim_{ h\rightarrow0}\displaystyle\frac{h}{\sin |h|}$$

which does not exist.