`BookProof.ChapterSphericalBesselODE.hasDerivAt_sbessel_scaled` (l : ℕ) {p x : ℝ} (hp : p ≠ 0) (hx : x ≠ 0) : HasDerivAt (fun s : ℝ => sbessel l (p * s)) (deriv (sbessel l) (p * x)

Proved

BookProof.ChapterSphericalBesselODE.hasDerivAt_sbessel_scaled

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSphericalBesselODE.

BookProof.ChapterSphericalBesselODE.hasDerivAt_sbessel_scaled (l : ℕ) {p x : ℝ} (hp : p ≠ 0) (hx : x ≠ 0) : HasDerivAt (fun s : ℝ => sbessel l (p * s)) (deriv (sbessel l) (p * x) * p) x

Formalization note: Lean 4 identifier BookProof.ChapterSphericalBesselODE.hasDerivAt_sbessel_scaled.

Preamble

-- Generated from ChapterSphericalBesselODE.lean — theorem BookProof.ChapterSphericalBesselODE.hasDerivAt_sbessel_scaled
import Mathlib
import Definitions.Def_ChapterSphericalBesselODE
import Definitions.Def_ChapterSphericalBessel
open BookProof.ChapterSphericalBessel
open BookProof.ChapterSphericalBesselODE



open BookProof.ChapterSphericalBessel

Formal statement

theorem BookProof.ChapterSphericalBesselODE.hasDerivAt_sbessel_scaled (l : ℕ) {p x : ℝ} (hp : p ≠ 0) (hx : x ≠ 0) :
    HasDerivAt (fun s : ℝ => sbessel l (p * s)) (deriv (sbessel l) (p * x) * p) x := by sorry

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