Theorems · Theorem · real analysis

hasStrictFDerivAt_finsetProd

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {ι : Type u_5} {𝔸' : Type u_7} [inst_1 : NormedCommRing 𝔸']
  [inst_2 : NormedAlgebra 𝕜 𝔸'] {u : Finset ι} [inst_3 : DecidableEq ι] [Finite ι] {x : ι → 𝔸'},
  HasStrictFDerivAt (fun x => ∏ i ∈ u, x i) (∑ i ∈ u, (∏ j ∈ u.erase i, x j) • ContinuousLinearMap.proj i) x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Mul

Cited by

3 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedCommRingNormedAlgebraDecidableEqFinite