Theorems · Theorem · real analysis

iteratedDerivWithin_eq_iterate

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {n : ℕ} {f : 𝕜 → F} {s : Set 𝕜} {x : 𝕜},
  iteratedDerivWithin n f s x = (fun g => derivWithin g s)^[n] f x

The n-th iterated derivative within a set with unique derivatives can be obtained by iterating n times the differentiation operation.

Defined in

Mathlib.Analysis.Calculus.IteratedDeriv.Defs

Cited by

2 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace