Theorems · Theorem · real analysis

fderiv_const_mul

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {x : E} {𝔸 : Type u_5} [inst_3 : NormedRing 𝔸] [inst_4 : NormedAlgebra 𝕜 𝔸] {a : E → 𝔸},
  DifferentiableAt 𝕜 a x → ∀ (b : 𝔸), fderiv 𝕜 (fun y => b * a y) x = b • fderiv 𝕜 a x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Mul

Cited by

0 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedRingNormedAlgebra