Theorems · Theorem · real analysis

HasDerivAt.mul_const

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

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

8 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedRingNormedAlgebra