A derivative was any chemical compound derived from another.
In 2268, Doctor Leonard McCoy believed a theragen derivative held the key to mitigating the effects of interphase, and hoped the next one he tried would be the one. He eventually developed the correct remedy with the aid of Christine Chapel. Diluted with alcohol, it had the ability to deaden the connection between certain nerves and the brain. (TOS: "The Tholian Web")
Later that year, McCoy noted that an antidote for the Yonada's Oracle's effects tasted like an ancient herb derivative. (TOS: "For the World is Hollow and I Have Touched the Sky")
In 2367, Data reported that the explosive used in a bomb was a triceron derivative. (TNG: "Reunion")
In 2374, The Doctor provided Chakotay with a highly potent animazine derivative, to be taken should he feel sleep. (VOY: "Waking Moments")