The formulas for the relativistic transformation of velocity, acceleration, and higher derivatives are obtained in a simple way using the concept of the differential of a function. LetF0be a Lorentz transformation. Given the transformationFn, this paper describes a process by which one can construct the transformationFn+1. Starting with the given Lorentz transformationF0, this process yields a sequence of transformationsF1,F2,F3,... . Although the Lorentz transformationF0is linear,Fn, for alln>0, are nonlinear. The differentials of these nonlinear transformations give the correct transformation formulas for velocity, acceleration, and all higher‐order derivatives.