apply hasDerivAt_deriv_iff.mpr
σ₁ σ₂ t : ℝ
t_ne_zero : t ≠ 0
diff : ∀ (σ : ℝ), DifferentiableAt ℂ ζ (↑σ + ↑t * I)
x : ℂ
hx : x ∈ (fun y => ↑y + ↑t * I) '' [[σ₁, σ₂]]
⊢ HasDerivAt (deriv ζ) (deriv (deriv ζ) x) x
σ₁ σ₂ t : ℝ
t_ne_zero : t ≠ 0
diff : ∀ (σ : ℝ), DifferentiableAt ℂ ζ (↑σ + ↑t * I)
x : ℂ
hx : x ∈ (fun y => ↑y + ↑t * I) '' [[σ₁, σ₂]]
⊢ DifferentiableAt ℂ (deriv ζ) x