∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {g : 𝕜 → E} {f : 𝕜 → 𝕜} {s t : Set 𝕜} {x : 𝕜},
  ContDiffWithinAt 𝕜 3 g t (f x) →
    ContDiffWithinAt 𝕜 3 f s x →
      UniqueDiffOn 𝕜 t →
        UniqueDiffOn 𝕜 s →
          x ∈ s →
            Set.MapsTo f s t →
              iteratedDerivWithin 3 (g ∘ f) s x =
                derivWithin f s x ^ 3 • iteratedDerivWithin 3 g t (f x) +
                    3 • iteratedDerivWithin 2 f s x • derivWithin f s x • iteratedDerivWithin 2 g t (f x) +
                  iteratedDerivWithin 3 f s x • derivWithin g t (f x)