This thesis is concerned with the designing of an nth order adaptive integral variable structure derivative estimator (AIVSDE). The proposed estimator's scheme is in fact a modified and extended version of the existing AIVSDE. The new proposed AIVSDE can be used as a direct nth differentiator for a smooth signal which has n continuous and bounded derivatives. The adaptive algorithm is utilized for the switching gain to remove the requirement for a priori knowledge about the upper bound of the derivative of the input signal. The stability of the redesigned first order, the second order, and the nth order derivative's estimation is guaranteed by the proposed scheme. An example is demonstrated for showing the applicability of the proposed AIVSDE.