∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} {𝔸 : Type u_3} [inst_1 : NormedRing 𝔸]
  [inst_2 : NormedAlgebra 𝕜 𝔸] {c d : 𝕜 → 𝔸},
  DifferentiableWithinAt 𝕜 c s x →
    DifferentiableWithinAt 𝕜 d s x → derivWithin (c * d) s x = derivWithin c s x * d x + c x * derivWithin d s x