How do I check if the partial derivative (according to vector ex) exists in a piecewise function? Consider this function $f$:
\begin{cases} \frac{x+y}{x^2+y^2} & (x,y) \neq (0,0)\\ 0 & (x,y) = (0,0)\\ \end{cases}
I calculated the derivative by definition for the first expression and I obtained 0. In order to check if the derivative exists do I have to calculate the same limit but considering the second exprssion? In this case f(0,0) is not relevant to check whether the derivative exists, right? The limit by definition of derivative (I don't know what to call it) has to be the same when I consider either expression but t -> 0 in either limit, right?