Theorems · Theorem · real analysis

iteratedDerivWithin_succ

∀ {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},
  iteratedDerivWithin (n + 1) f s = derivWithin (iteratedDerivWithin n f s) s

The n+1-th iterated derivative within a set with unique derivatives can be obtained by differentiating the n-th iterated derivative.

Defined in

Mathlib.Analysis.Calculus.IteratedDeriv.Defs

Cited by

11 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace