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.
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