'fat-derived' originates from English, formed by combining 'fat' (the word 'fat' from Old English 'fætt'/'fæt') and 'derived' (the past participle of 'derive', ultimately from Latin 'derivare').

'fat' changed from Old English 'fætt' to Middle English 'fat' and eventually modern English 'fat'. 'Derive' came into English via Old French (dériver) from Latin 'derivare'; the past participle 'derived' is used in compounds like 'fat-derived'.

Individually, 'fat' originally referred to being well-fed or to fatty tissue, and 'derive' originally meant 'to draw off or obtain from'; together the compound came to mean 'obtained from fat' and is used in scientific/technical contexts to indicate origin from fat.