A robust identification-based state derivative estimation method for uncertain nonlinear systems is developed. The identifier architecture consists of a recurrent multilayer dynamic neural network which approximates the system dynamics online, and a continuous robust feedback Robust Integral of the Sign of the Error (RISE) term which accounts for modeling errors and exogenous disturbances. Numerical simulations provide comparisons with existing robust derivative estimation methods including: a high gain observer, a 2-sliding mode robust exact differentiator, and numerical differentiation methods, such as backward difference and central difference.