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Theorems Β· Theorem Β· real analysis

iteratedDeriv_const_mul_field

βˆ€ {π•œ : Type u_1} [inst : NontriviallyNormedField π•œ] {x : π•œ} {π•œ' : Type u_6} [inst_1 : NormedDivisionRing π•œ']
  [inst_2 : NormedAlgebra π•œ π•œ'] {n : β„•} (c : π•œ') (f : π•œ β†’ π•œ'),
  iteratedDeriv n (fun x => c * f x) x = c * iteratedDeriv n f x

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

Defined in
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas
Cited by
0 results in Mathlib
Foundations
Depth 182 from the axioms Β· uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedDivisionRingNormedAlgebra
Mathlib docsSourceLoogleLeanSearch

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NontriviallyNormedField Β· cited by 8742NontriviallyNormedFieldNormedAlgebra Β· cited by 1165NormedAlgebraNormedDivisionRing Β· cited by 360NormedDivisionRingiteratedDeriv Β· cited by 188iteratedDeriviteratedDerivWithin_univ Β· cited by 16iteratedDerivWithin_univiteratedDerivWithin_const_mul_field Β· cited by 1iteratedDerivWithin_const…iteratedDeriv_const_mul_fieldCITED BYCITES

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