The simplest method of improving selectivity is to derivatively alter the spectrum; this procedure reduces spectral interference and, as a result, improves the assay's selectivity. It has been shown that derivative improves selectivity when first, second, third, and fourth derivatives are tried. Digital data derivatization is a well-known method for extracting useful signals from noisy data. Without requiring extraction or separation, the research study  refers that application of higher order derivative spectrophotometry enables the simultaneous identification of cerium, lanthanum, and samarium rare earth elements. The established procedure is straightforward, sensitive, and effective. Using this technique can find out the concentrations of Ce, La, and Sm species in rare earth oxides obtained from Egyptian industrial phosphogypsum. The complexes' development and measured were best impacted by studying wavelength, pH, surfactant, molar ratio, initial chrome azurol S (CAS) dye concentration, and finally the linear calibration graphs in the 0.25 to 12 µg/ml range for Sm, Ce, and La. The molar absorptivity (ɛ) at the wavelength λmax of the maximum absorbance of the colored species was 0.092, 0.1 and 0.11, relative standard deviation (RSD%) was 1.868, 0.026, and 0.051 and percentage error was 0.98, 0.53 and 0.51 % for Sm, Ce and La respectively.