Theorems · Theorem · real analysis

iteratedDerivWithin_mul_const_field

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

A variant of iteratedDerivWithin_mul_const without differentiability assumption when the scalar multiplication is by division ring elements.

Defined in

Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedDivisionRingNormedAlgebra