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

Lemma derivable_pt_lim_comp_2d : forall f1 f2 f3 x l1x l1y l2 l3, differentiable_pt_lim f1 (f2 x) (f3 x) l1x l1y -> derivable_pt_lim f2 x l2 -> derivable_pt_lim f3 x l3 -> derivable_pt_lim (fun t => f1 (f2 t) (f3 t)) x (l1x * l2 + l1y * l3).