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Theorems · Theorem · real analysis

HasDerivAt.fun_add

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f g : 𝕜 → F} {f' g' : F} {x : 𝕜},
  HasDerivAt f f' x → HasDerivAt g g' x → HasDerivAt (fun i => f i + g i) (f' + g') x

Eta-expanded form of HasDerivAt.add

Defined in
Mathlib.Analysis.Calculus.Deriv.Add
Cited by
0 results in Mathlib
Foundations
Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace
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NormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldHasDerivAt · cited by 493HasDerivAtHasDerivAt.add · cited by 13HasDerivAt.addHasDerivAt.fun_addCITED BYCITES

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