1610s, from French productif (16c.) and directly from Medieval Latin productivus "fit for production," from Latin product-, past participle stem of producere (see produce (v.)). Related: Productively; productiveness.
word-forming element used since 18c. (but most productively in 20c.) and typically meaning "kind of, resembling, like but not really, as if;" from Latin quasi "as if, as it were" (see quasi).