A comprehensive study of derivative methods for the peak search analysis of X-ray diffraction data was made to determine the relative merits of the methods. The peak positions were best determined by the cubic first derivative method which had an intrinsic error ≤ 0.001°, and random error ∼ ± 0.003 ° to 0.02 ° depending on the counting statistical noise. The quadratic/cubic second derivative method had the highest resolution with a separation limit ≥ 1/2w (w = full width at half maximum). An effective algorithm combining the cubic first derivative and the quadratic/cubic second derivative methods was developed for high precision and resolution. The method uses a full screen menu for parameter selection, and the entire peak search analysis including peak identification and position determination, and graphic and numeric display of results at the color terminal is completed in a few seconds using a time sharing mode on an IBM 3083 central processing unit. The combined derivative method should be also applicable to other spectra such as gamma-rays, X-ray fluorescence, optical, infrared, ESCA, Mossbauer, etc.