∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} (p : Polynomial 𝕜),
  UniqueDiffWithinAt 𝕜 s x →
    fderivWithin 𝕜 (fun x => Polynomial.eval x p) s x =
      ContinuousLinearMap.smulRight 1 (Polynomial.eval x (Polynomial.derivative p))