Theorems · Theorem · real analysis

HasDerivAtFilter.fun_const_smul

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {L : Filter (𝕜 × 𝕜)} {R : Type u_2} [inst_3 : Monoid R]
  [inst_4 : DistribMulAction R F] [SMulCommClass 𝕜 R F] [ContinuousConstSMul R F] (c : R),
  HasDerivAtFilter f f' L → HasDerivAtFilter (fun i => c • f i) (c • f') L

Eta-expanded form of HasDerivAtFilter.const_smul

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

0 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceMonoidDistribMulActionSMulCommClassContinuousConstSMul