1816, transitive, "make different; be what distinguishes between," from Medieval Latin differentiatus, past participle of differentiare, from Latin differentia "diversity, difference" (see difference).
Originally a mathematical term, "obtain the differential coefficient of;" intransitive sense of "acquire a distinct and separate character" is by 1874. Non-technical transitive sense of "discriminate between by observing or describing the difference between" is from 1876; earlier, difference had been used as a verb in this sense. Related: Differentiated; differentiating.