∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {n : ℕ} {x : 𝕜} {𝔸 : Type u_5} [inst_1 : NormedRing 𝔸]
  [inst_2 : NormedAlgebra 𝕜 𝔸] {f g : 𝕜 → 𝔸},
  ContDiffAt 𝕜 (↑n) f x →
    ContDiffAt 𝕜 (↑n) g x →
      iteratedDeriv n (fun x => f x * g x) x =
        ∑ i ∈ Finset.range (n + 1), ↑(n.choose i) * iteratedDeriv i f x * iteratedDeriv (n - i) g x