"tending to exhaust all parts or phases, thorough," especially of a writing or speech which leaves no part of its subject unexamined, 1789, from exhaust (v.) + -ive. Related: Exhaustively; exhaustiveness.
1530s, "to draw off or out, to use up completely," from Latin exhaustus, past participle of exhaurire "draw off, take away, use up, empty," from ex "off" (see ex-) + haurire "to draw up" (as water), from PIE *heusio- "to scoop." Meaning "make weak or helpless, as by fatigue" is from 1630s. Related: Exhausted; exhausting; exhaustible.
word-forming element making adjectives from verbs, meaning "pertaining to, tending to; doing, serving to do," in some cases from Old French -if, but usually directly from Latin adjectival suffix -ivus (source also of Italian and Spanish -ivo). In some words borrowed from French at an early date it has been reduced to -y (as in hasty, tardy).
<a href="https://www.etymonline.com/word/exhaustive">Etymology of exhaustive by etymonline</a>
Harper, D. (n.d.). Etymology of exhaustive. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/exhaustive