Theorems · Theorem · global analysis

fderivWithin_add

∀ {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] {f g : E → F}
  {x : E} {s : Set E},
  UniqueDiffWithinAt 𝕜 s x →
    DifferentiableWithinAt 𝕜 f s x →
      DifferentiableWithinAt 𝕜 g s x → fderivWithin 𝕜 (f + g) s x = fderivWithin 𝕜 f s x + fderivWithin 𝕜 g s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Add

Cited by

4 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace