I have the following problem of two variables differentiability:
The value of function at $(0,0)$ is $0$.I have proved that the function is continuous at $(0,0)$. Also, both of the partial derivatives exists and equal to zero. But, I am not able to prove the differentiability of the above Function. I know that the continuous partial derivatives means that the function is differentiable but isn't the existence of partial derivatives proves continuity of partial derivatives. Because, I have obtained the partial derivatives using the limit definition. I think the equality of both partial derivatives means the continuity of them. I am really confused in this problem. Please help and give me set of advice while checking the differentiability of two variables function. Thanks in advance.