simp_rw [← Complex.real_smul]
𝕜 : Type u_1
E : Type u_2
inst✝³ : NontriviallyNormedField 𝕜
inst✝² : NormedAlgebra 𝕜 ℝ
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℝ E
x dx : ℝ
⊢ cexp (↑(2 * π * x) * I) * (fderiv ℝ (fun x => ↑(2 * π * x) * I) x) dx = ↑(2 * π * dx) * (I * cexp (↑(2 * π * x) * I))
𝕜 : Type u_1
E : Type u_2
inst✝³ : NontriviallyNormedField 𝕜
inst✝² : NormedAlgebra 𝕜 ℝ
inst✝¹ : NormedAddCommGroup E
inst✝ : NormedSpace ℝ E
x dx : ℝ
⊢ cexp ((2 * π * x) • I) * (fderiv ℝ (fun x => (2 * π * x) • I) x) dx = (2 * π * dx) • (I * cexp ((2 * π * x) • I))