Theorems · Theorem · real analysis

hasFDerivAt_multiset_prod

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {ι : Type u_5} {𝔸' : Type u_7} [inst_1 : NormedCommRing 𝔸']
  [inst_2 : NormedAlgebra 𝕜 𝔸'] [inst_3 : DecidableEq ι] [Finite ι] {u : Multiset ι} {x : ι → 𝔸'},
  HasFDerivAt (fun x => (Multiset.map x u).prod)
    (Multiset.map (fun i => (Multiset.map x (u.erase i)).prod • ContinuousLinearMap.proj i) u).sum x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Mul

Cited by

2 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedCommRingNormedAlgebraDecidableEqFinite