Theorems · Theorem · real analysis

derivWithin_mul_const

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} {𝔸 : Type u_3} [inst_1 : NormedRing 𝔸]
  [inst_2 : NormedAlgebra 𝕜 𝔸] {c : 𝕜 → 𝔸},
  DifferentiableWithinAt 𝕜 c s x → ∀ (d : 𝔸), derivWithin (fun y => c y * d) s x = derivWithin c s x * d

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

1 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedRingNormedAlgebra