Higher order sliding-mode differentiators have received a great deal of attention in the literature. For the case of reconstructing the first derivative, theoretical convergence conditions for the differentiator are available from which differentiator parameters may be selected. For the case of higher order derivatives, some parameter settings have been suggested for differentiators of certain order but there is no tuning algorithm available to determine convergent parameters for differentiators of arbitrary order. Whilst recognising the strong theoretical properties of sliding-mode differentiators, practitioners report difficulties in achieving wide envelope performance from a single set of differentiator parameters. This paper proposes a constructive design paradigm to generate differentiator parameters which is seen to provide a natural framework to facilitate simple online adaptation of the chosen gains. Simulation experiments as well as experimental results are presented to demonstrate the proposed approach.