2nd order partial differentiation

Question

The following is the question:$$f(x,y)=|x^2-y^2|\space \space Find\space f_{xy}(0,0)$$ I have found $f_y(0,0)=0$ and I am stuck here $f_y(h,0)=\lim_{k\to0}\frac{|h^2-k^2|-h^2}{k}$, but if I take $h>k$, $f_y=0$ else $f_y=-\infty$. Am I correct ?? Please help