So I have a function

x^{3}y - xy^{3 }__________

x^{2}+ y^{2 }

for all (x,y) not equal to (0,0)

and the function is equal to 0 for (x,y) = (0,0) (Basically to make the function continuous)

I need to do a limit definition of the function above

f_{x}(0,0) =

lim(h->0)

f(h,0) - f(0,0)

_____________

h

And the same for f_{y }

I need to show that f_{x}(0,0) = f_{y}(0,0) = 0

I was never good at limit derivatives in Calculus 1 because i already knew the shortcuts, so I am completely lost on how to do this.

Sorry for the format, I could not get it the align right