In the set Tn of trigonometric polynomials fn of order n with complex coefficients, we consider Weyl (fractional) derivatives fn(α) of real nonnegative order α. The inequality ║Dθαfn║p ≤ Bn(α, θ)p║fn║p for the Weyl-Szegő operator Dθαfn(t) = fnα (t)cosθ + fnα (t) sin θ in the set Tn of trigonometric polynomials is a generalization of Bernstein’s inequality. Such inequalities have been studied for 90 years. G. Szegő obtained the exact inequality ║f′n cos θ + f ′n sin θ║∞ ≤ n║fn║∞ in 1928. Later, A. Zygmund (1933) and A.I.Kozko (1998) showed that, for p ≥ 1 and real α ≥ 1, the constant Bn(α, θ)p equals nα for all θ ∈ ℝ. The case p = 0 is of additional interest because it is in this case that Bn(α, θ)p is largest over p ∈ [0, ∞]. In 1994 V. V. Arestov showed that, for θ = π/2 (in the case of the conjugate polynomial) and integer nonnegative α, the quantity Bn(α,π/2)0 grows exponentially in n as 4n+o(n). It follows from his result that the behavior of the constant for θ ≠ 2πk is the same. However, in the case θ = 2πo and α ∈ ℕ, Arestov showed in 1979 that the exact constant is nα. The author investigated Bernstein’s inequality in the case p = 0 for positive noninteger α earlier (2018). The logarithmic asymptotics of the exact constant was obtained: $$\sqrt[n]{{{B_n}{{(\alpha,\,0)}_0}}} \to 4$$ as n → ∞. In the present paper, this result is generalized to all θ ∈ ℝ.