simp only [derivCLM_apply]
F : Type u_1
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedSpace ℂ F
inst✝ : CompleteSpace F
f : 𝓢(ℝ, F)
ξ : ℝ
h_cover : AECover volume Filter.atTop fun i => Set.Ioc (-↑i) ↑i
⊢ Filter.Tendsto
    (fun n =>
      ∫ (x : ℝ) in -↑n..↑n,
        ↑(Real.fourierChar (Multiplicative.ofAdd (-(x * ξ)))) • ((derivCLM ℝ) f) x -
          (2 * ↑π * I * ↑ξ) • ↑(Real.fourierChar (Multiplicative.ofAdd (-(x * ξ)))) • f x)
    Filter.atTop (nhds 0)
F : Type u_1
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedSpace ℂ F
inst✝ : CompleteSpace F
f : 𝓢(ℝ, F)
ξ : ℝ
h_cover : AECover volume Filter.atTop fun i => Set.Ioc (-↑i) ↑i
⊢ Filter.Tendsto
    (fun n =>
      ∫ (x : ℝ) in -↑n..↑n,
        ↑(Real.fourierChar (Multiplicative.ofAdd (-(x * ξ)))) • deriv (⇑f) x -
          (2 * ↑π * I * ↑ξ) • ↑(Real.fourierChar (Multiplicative.ofAdd (-(x * ξ)))) • f x)
    Filter.atTop (nhds 0)