Theorems · Theorem · real analysis
DifferentiableAt.fun_finset_prod
Deprecated since 2026-04-08Use DifferentiableAt.fun_finsetProd instead.
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {ι : Type u_2} {𝔸' : Type u_3} [inst_1 : NormedCommRing 𝔸']
[inst_2 : NormedAlgebra 𝕜 𝔸'] {u : Finset ι} {f : ι → 𝕜 → 𝔸'},
(∀ i ∈ u, DifferentiableAt 𝕜 (f i) x) → DifferentiableAt 𝕜 (fun x => ∏ i ∈ u, f i x) xAlias of DifferentiableAt.fun_finsetProd.
- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- NontriviallyNormedFieldstatement · cited by 8,742
- Finset.prodstatement · cited by 2,356
- NormedAlgebrastatement · cited by 1,165
- DifferentiableAtstatement · cited by 617
- NormedCommRingstatement · cited by 218
- DifferentiableAt.fun_finsetProdproof · cited by 4
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