prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not." Often euphemistic (such as untruth for "lie").
The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.
It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.
1610s, "serving to produce," from French productif (16c.) and directly from Medieval Latin productivus "fit for production," from Latin product-, past-participle stem of producere "bring forth" (see produce (v.)). Meaning "fertile, producing abundantly" is by 1706. Related: Productively; productiveness.
<a href="https://www.etymonline.com/word/unproductive">Etymology of unproductive by etymonline</a>
Harper, D. (n.d.). Etymology of unproductive. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/unproductive