Added by Exodus on January 26, 2001 at 23:36:35:
the slope of any line at a point is given by the first derivative of the function evaluated at that point.
f(x,y) = x^2 +y^3 +xy + 6x + 10y + 5
partial x derivative:
d(f(x,y,))/dx = 2x +y + 6
partial y derivatives
d(f(x,y))/dx = 3y^2 + x + 10
a unique solution exists iff
d^2f(x,y)/dxdy = d^2f(x,y)/dydx