I know how to get the first partial derivative of a piecewise function at a certain point but I'm unsure how to get the second one.
I'm trying to do it for the following function:
$f(x,y) = \begin{cases} \frac{x^2-y^2}{x^2+y^2} & \text{if } (x,y) \neq (0,0)\\ 0 & \text{if } (x,y) = (0,0) \end{cases}$
I want to calculate the following partial derivatives: $\frac{\partial^2 f}{\partial x \partial y}(0,0)$ and $\frac{\partial^2 f}{\partial y \partial x}(0,0)$
I think it's: $\frac{\partial^2 f}{\partial x \partial y}(0,0) = \lim_{h \to 0} \frac{ \frac{\partial f}{\partial x}(0,h) - \frac{\partial f}{\partial x}(0,0)}{h}$
I don't know how I should go about calculating this though.