∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f g : 𝕜 → F} {x : 𝕜} {s : Set 𝕜},
  DifferentiableWithinAt 𝕜 f s x →
    DifferentiableWithinAt 𝕜 g s x → derivWithin (fun y => f y + g y) s x = derivWithin f s x + derivWithin g s x