Theorems · Theorem · global analysis

CPolynomialOn.fderiv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type v} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {s : Set E}, CPolynomialOn 𝕜 f s → CPolynomialOn 𝕜 (fderiv 𝕜 f) s

If a function is polynomial on a set s, so is its Fréchet derivative.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Analytic

Cited by

2 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace