word-forming element, especially in scientific compounds, meaning "life, life and," or "biology, biology and," or "biological, of or pertaining to living organisms or their constituents," from Greek bios "one's life, course or way of living, lifetime" (as opposed to zoe "animal life, organic life"), from PIE root *gwei- "to live."
The correct usage is that in biography, but since c. 1800 in modern science it has been extended to mean "organic life," as zoo-, the better choice, is restricted in modern use to animal, as opposed to plant, life. Both are from the same PIE root. Compare biology.
1560s, chymist, "alchemist," from French chimiste, from Medieval Latin chimista, reduced from alchimista (see alchemy). The modern spelling is from c. 1790. The meaning "chemical scientist, person versed in chemistry" is from 1620s; the looser meaning "dealer in medicinal drugs" is from 1745, mostly in British English.
<a href="https://www.etymonline.com/word/biochemist">Etymology of biochemist by etymonline</a>
Harper, D. (n.d.). Etymology of biochemist. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/biochemist