1. The problem statement, all variables and given/known data Determine if f(x,y) = ((x-y)4 +x3 +xy2)/(x2+y2) [f(x,y = 0 @ (0,0)] is differentiable at the origin. 2. Relevant equations x = (0,0) 3. The attempt at a solution A function is differentiable at x if f(x+Δx) - f(x) = AΔx + |Δx|R(x) Where A are constant coefficients of the vector Δx, and R(Δx) → 0 as Δx → 0. A couple of questions. 1) in order to solve this, should I set A = [∂f/∂x, ∂f/∂y] evaluated at (0,0)? My literature claims A just needs to be "some constant", not literally the partials evaluated at that point. A bit confused there. 2) Just to double check, if the first step is determining ∂f/∂x at a given point, I am free to set y=0 BEFORE calculating the partial wrt x, right?