Definition differentiable_pt (f : R -> R -> R) (x y : R) :=
  exists lx, exists ly, differentiable_pt_lim f x y lx ly.

Lemma differentiable_pt_lim_comp : forall f1 f2 f3 x y l1x l1y l2x l2y l3x l3y, differentiable_pt_lim f1 (f2 x y) (f3 x y) l1x l1y -> differentiable_pt_lim f2 x y l2x l2y -> differentiable_pt_lim f3 x y l3x l3y -> differentiable_pt_lim (fun u v => f1 (f2 u v) (f3 u v)) x y (l1x * l2x + l1y * l3x) (l1x * l2y + l1y * l3y).