early 15c., in a now-obsolete medical sense, "having the property of drawing off or away," from Old French derivatif (15c.) and directly from Late Latin derivativus, from derivat-, past-participle stem of Latin derivare "to lead or draw off" (see derive). Meaning "taken or having proceeded from another or others, secondary" is from 1520s. Related: Derivatively; derivativeness.
mid-15c., "a derived word or form, a word formed immediately or remotely from another or a root," from derivative (adj.). General sense of "that which is derived or deduced from another" is from 1590s. Mathematical sense, "a derivative function," is from 1670s. In chemistry, "compound that can be made from a parent compound by replacement of one atom with another atom or group of atoms," by 1855.