Theorems · Theorem · real analysis

derivWithin_pi

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} {ι : Type u_1} {E' : ι → Type u_2}
  [inst_1 : (i : ι) → NormedAddCommGroup (E' i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E' i)] {φ : 𝕜 → (i : ι) → E' i},
  (∀ (i : ι), DifferentiableWithinAt 𝕜 (fun x => φ x i) s x) →
    derivWithin φ s x = fun i => derivWithin (fun x => φ x i) s x

Defined in

Mathlib.Analysis.Calculus.Deriv.Prod

Cited by

0 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace