Basic bivariate question

1. Mar 12, 2005

MaximumTaco

given f(x,y) = (xy+(x^3))/(x^2+xy)

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.