'protein-derived' is a compound of 'protein' and 'derived'. 'Protein' originates from Greek, specifically the word 'proteios' meaning 'primary' (coined in modern use as 'protein' in the early 19th century), and 'derived' originates from Latin, specifically the verb 'derivare' meaning 'to draw off or divert'.

'protein' was coined in modern scientific English (c. 1838) from Greek 'proteios' ('primary'); 'derived' came into English via Old French/Latin ('derivare' → Old French 'deriver' → Middle/Modern English 'derive'), and the compound 'protein-derived' developed by combining these two elements in scientific contexts to mean 'originating from protein'.

Originally 'derive' (from Latin) had senses like 'to draw off' (e.g., water) and 'to obtain from'; over time it generalized to 'originate from' or 'be obtained from', so 'protein-derived' now specifically means 'originating from or obtained from proteins'.