product (n.)

early 15c., producen, "develop, proceed, extend, lengthen out," from Latin producere "lead or bring forth, draw out," figuratively "to promote, empower; stretch out, extend," from pro "before, forth" (from PIE root *per- (1) "forward," hence "in front of, before, forth") + ducere "to bring, lead" (from PIE root *deuk- "to lead").

The sense of "bring into being or existence" is from late 15c. That of "put (a play) on stage" is from 1580s. Of animals or plants, "generate, bear, bring forth, give birth to," 1520s. The meaning "cause, effect, or bring about by mental or physical labor" is from 1630s. In political economy, "create value; bring goods, manufactures, etc. into a state in which they will command a price," by 1827. Related: Produced; producing.

also byproduct, "secondary or additional product;" 1849, from by + product.