Theorems · Theorem · real analysis

iteratedDerivWithin_comp_const_smul

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {n : ℕ} {x : 𝕜} {s : Set 𝕜},
  x ∈ s →
    UniqueDiffOn 𝕜 s →
      ∀ {f : 𝕜 → F},
        ContDiffOn 𝕜 (↑n) f s →
          ∀ (c : 𝕜),
            Set.MapsTo (fun x => c * x) s s →
              iteratedDerivWithin n (fun x => f (c * x)) s x = c ^ n • iteratedDerivWithin n f s (c * x)

Defined in

Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace