Theorems · Theorem · real analysis

iteratedDeriv_mul_const_field

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝕜' : Type u_6} [inst_1 : NormedDivisionRing 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {n : ℕ} (f : 𝕜 → 𝕜') (c : 𝕜'),
  iteratedDeriv n (fun x => f x * c) x = iteratedDeriv n f x * c

A variant of iteratedDeriv_mul_const without differentiability assumption when the multiplication is in a division ring.

Defined in

Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedDivisionRingNormedAlgebra