Theorems · Theorem · real analysis

derivWithin_fun_const_smul

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} {s : Set 𝕜} {R : Type u_2} [inst_3 : Monoid R]
  [inst_4 : DistribMulAction R F] [SMulCommClass 𝕜 R F] [ContinuousConstSMul R F] (c : R),
  DifferentiableWithinAt 𝕜 f s x → derivWithin (fun y => c • f y) s x = c • derivWithin f s x

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

2 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceMonoidDistribMulActionSMulCommClassContinuousConstSMul