1. The problem statement, all variables and given/known data Let f(x,y)=x3 + x2y + y3. Show that f is differentiable at (1,2). 2. Relevant equations A function f(x,y) is differentiable at a point (x0,y0) if the partial derivatives of f(x,y) are defined at (x0,y0) and if the following limiting condition holds: lim(x,y)-->(x0,y0) [ f(x,y) - f(x0,y0) - ∂f/∂x|(x0,y0)(x-x0) - ∂f/∂y|(x0,y0)(y-y0) ] / √( (x-x0)2 + (y-y0)2) = 0. 3. The attempt at a solution ∂f/∂x = 3x2 + 2xy ===> ∂f/∂x|(1,2) defined ∂f/∂y = 2x2 + 3y2 ===> ∂f/∂y|(1,2) defined But I'm having trouble with making lim(x,y)-->(1,2) = 0. I got it all the way to lim(x,y)-->(1,2) = (x3+x2y+y3+22 -7x-13y)/√((x-1)2+(x-2)2). I need to get rid of the denominator. I thought about rationalizing the denominator, but I don't that'll get me anywhere. Suggestions welcome.