Abstract: | In the present paper, we obtain estimations of convergence rate derivatives of the q-Bernstein polynomials Bn (f, qn ; x) approximating to f ′ (x) asn → ∞, which is a generalization of that relating the classical case qn = 1. On the other hand, we study the convergence properties of derivatives of the limit q-Bernstein operators B ∞ (f, q; x) as q → 1 . |