Theorems · Theorem · real analysis

HasDerivWithinAt.clm_apply

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {x : 𝕜} {s : Set 𝕜} {G : Type u_2} [inst_3 : NormedAddCommGroup G]
  [inst_4 : NormedSpace 𝕜 G] {c : 𝕜 → F →L[𝕜] G} {c' : F →L[𝕜] G} {u : 𝕜 → F} {u' : F},
  HasDerivWithinAt c c' s x →
    HasDerivWithinAt u u' s x → HasDerivWithinAt (fun y => (c y) (u y)) (c' (u x) + (c x) u') s x

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

1 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace