Some asymptotic representations for the truncation error for the Lagrangian numerical differentiation are presented, when the ratio of the distance between each interpolation node and the differentiated point to step-parameter h is known. Furthermore, if the sampled values of the function at these interpolation nodes have perturbations which are bounded by ε, a method for determining step-parameter h by means of perturbation bound ε and order n of interpolation is provided to saturate the order of approximation. And all the investigations in this paper can be generalized to the set of quasi-uniform nodes.