Theorems · Theorem · real analysis

HasFDerivWithinAt.prodMk

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {G : Type u_4}
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {f₁ : E → F} {f₁' : E →L[𝕜] F} {x : E} {s : Set E}
  {f₂ : E → G} {f₂' : E →L[𝕜] G},
  HasFDerivWithinAt f₁ f₁' s x →
    HasFDerivWithinAt f₂ f₂' s x → HasFDerivWithinAt (fun x => (f₁ x, f₂ x)) (f₁'.prod f₂') s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Prod

Cited by

17 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace