Theorems · Theorem · real analysis

Polynomial.derivWithin_aeval

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} {R : Type u_1} [inst_1 : CommSemiring R]
  [inst_2 : Algebra R 𝕜] (q : Polynomial R),
  UniqueDiffWithinAt 𝕜 s x →
    derivWithin (fun x => (Polynomial.aeval x) q) s x = (Polynomial.aeval x) (Polynomial.derivative q)

Defined in

Mathlib.Analysis.Calculus.Deriv.Polynomial

Cited by

0 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldCommSemiringAlgebra