Theorems · Theorem · real analysis

IsSymmSndFDerivAt.iteratedFDeriv_cons

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} {F : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x v w : E}
  {hf : IsSymmSndFDerivAt 𝕜 f x}, (iteratedFDeriv 𝕜 2 f x) ![v, w] = (iteratedFDeriv 𝕜 2 f x) ![w, v]

Defined in

Mathlib.Analysis.Calculus.FDeriv.Symmetric

Cited by

0 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace