Theorems · Theorem · real analysis

iteratedFDeriv_comp_const_smul

∀ {𝕜 : Type u_1} [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}
  {i : ℕ} (a : 𝕜),
  ContDiff 𝕜 (↑i) f → (iteratedFDeriv 𝕜 i fun z => f (a • z)) = fun x => a ^ i • iteratedFDeriv 𝕜 i f (a • x)

Defined in

Mathlib.Analysis.Calculus.ContDiff.Operations

Cited by

1 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace