The most straightforward technique to boost selectivity is to derivatively modify the spectrum; this process can be used to eliminate spectral interference, which in turn raises the assay's selection. Digital data derivatization is a well-known technique for separating valuable signals from noisy data, and it has been observed that the first derivative increases selectivity when first, second, third, and fourth derivatives are tested.

This research study is considered by the utilization of higher order derivative spectrophotometry for the simultaneous determination of lutetium, terbium and thallium rare earth elements without extraction or separation. The developed procedure is simple, reliable and sensitive. This method allows the determination of lutetium and terbium in a sample of phosphate rock. Optimum factors affecting the formation and measuring of the complexes such as wavelength, pH, initial dye concentration, molar ratio and linear calibration graphs in the range 0.25 to 12 µg -1 for Lu and Tb was obtained whereas relative standard deviation RSD% was 1.75 and 1.58 and percentage error 1.01 % and 0.91 % respectively.