This paper deals with online numerical differentiation of a noisy time signal where new higher order sliding mode differentiators are proposed. The key point of these algorithms is to include a dynamic on the differentiator parameters. These dynamics tune-up automatically the algorithm gains in real-time. Convergence properties of the new schemes are derived using a Lyapunov approach. Their effectiveness is illustrated via simulations and experimental tests, where comparative studies are performed between classical schemes and the new ones. Such algorithms are also used in the feedback control of an electrohydraulic system.