Theorems · Theorem · real analysis

ContDiff.differentiable_iteratedFDeriv

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {n : WithTop ℕ∞} {m : ℕ}, ↑m < n → ContDiff 𝕜 n f → Differentiable 𝕜 fun x => iteratedFDeriv 𝕜 m f x

If f is C^n then its m-times iterated derivative is differentiable for m < n.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Defs

Cited by

4 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace