This paper considers observer-based controller design for systems involving input derivatives. First, we analyze the class of systems with derivative inputs which appear naturally or in connection to other class of systems such as singular systems. Due to the presence of input derivatives, we provide a procedure to eliminate the derivative inputs in order to facilitate the process of stabilization by state feedback. The elimination procedure transfers the input derivatives in the output equations. However, we show that the observer can also be designed by using change of variables avoiding derivative inputs in the final observer equation. Consequently, we construct the observer based controller design and establish separation principle for input derivative systems. Numerical example is provided to support the theoretical result.