`BookProof.HarmonicOscillator.deriv_const_mul_fun` (c : ℂ) {f : ℝ → ℂ} (hf : ∀ x, DifferentiableAt ℝ f x) : deriv (fun x => c * f x) = fun x => c * deriv f x

Proved

BookProof.HarmonicOscillator.deriv_const_mul_fun

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHarmonicOscillatorEsa.

BookProof.HarmonicOscillator.deriv_const_mul_fun (c : ℂ) {f : ℝ → ℂ} (hf : ∀ x, DifferentiableAt ℝ f x) : deriv (fun x => c * f x) = fun x => c * deriv f x

Formalization note: Lean 4 identifier BookProof.HarmonicOscillator.deriv_const_mul_fun.

Preamble

-- Generated from ChapterHarmonicOscillatorEsa.lean — theorem BookProof.HarmonicOscillator.deriv_const_mul_fun
import Definitions.Def_ChapterHermiteFunctions
import Definitions.Def_ChapterStrichartzHermiteQG
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterHarmonicOscillatorEsa
open BookProof.HarmonicOscillator



open MeasureTheory Polynomial BookProof.HermiteCore BookProof.HermiteStrichartzQG
open BookProof.FarisLavine

Formal statement

theorem BookProof.HarmonicOscillator.deriv_const_mul_fun (c : ℂ) {f : ℝ → ℂ} (hf : ∀ x, DifferentiableAt ℝ f x) :
    deriv (fun x => c * f x) = fun x => c * deriv f x := by sorry

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