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I want to calculate df/dx (i.e. first partial derivative wrt x) at the origin.

f is undefined there, but i can still do it, right?

so, we get (x^2 + 2xy -y)/(x^2 +2xy +y^2)

I'm not really sure of where to go with this, though.

I think the basic definition of the derivative, i.e. lim (h->0) ((x+h)y + (x+h)^3)/((x+h)^2 + (x+h)y) could be the way to go.

Any advice would be appreciated.

The only specific techniques i understand are the "sandwich rule", Taylor polynomials, as well as basic differentiation etc, and the 1-var stuff like l'Hopital's rule. So please don't give me something like the epsilon-delta stuff for limits or anything else i won't understand.