Please consider to deliver a slight bit more information to the community forum than the teacher did deliver to you.
x y = -1
f[x_,y_] := 1/(1 + x y)
{x,y}={0,0}
then there are entries like Hessian which could be used once the task at hand is clarified.
Thank you, I saw it, but actually, it's not the thing, I'm asking about... I need the way to find the change of variables, to see this change and write it like an explicit function.
Perhaps your teacher was referring to this (or some other) demonstration:
http://demonstrations.wolfram.com/MorseSmaleFlowsOnATiltedTorus/
