Theorems · Theorem · real analysis

DifferentiableOn.finsetProd

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {s : Set 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, DifferentiableOn 𝕜 (f i) s) → DifferentiableOn 𝕜 (∏ i ∈ u, f i) s

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

2 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedCommRingNormedAlgebra