Theorems · Theorem · real analysis
DifferentiableAt.finsetProd
∀ {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 (∏ i ∈ u, f i) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommGroupproof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Finset.prodstatement and proof · cited by 2,356
- NormedAlgebrastatement and proof · cited by 1,165
- DifferentiableAtstatement and proof · cited by 617
- NormedCommRingstatement and proof · cited by 218
- Finset.prod_applyproof · cited by 70
- DifferentiableAt.fun_finsetProdproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Differentiable.finsetProdproof · cited by 1
- DifferentiableAt.finset_prodproof · cited by 0