'Arab-derived' is a compound formed from 'Arab' and the past-participle/participial adjective 'derived'. 'Arab' ultimately comes from Arabic 'ʿarab' (عرب) via Medieval Latin and Old French, and 'derive' comes from Latin 'derivare' ('de-' + 'rivus' meaning 'stream').

'Arab' entered English through Medieval Latin/Old French forms referring to the Arabian people/region and traces back to Arabic 'ʿarab' meaning 'desert-dweller' or 'nomad'. 'Derived' comes from Latin 'derivare', passed into Middle English via Old French and Late Latin, and is used here as a participial adjective to form compounds like 'Arab-derived'.

Originally the elements meant 'Arab' (the people/Arabic) and 'flowed from/extended from' (literally 'derived from a stream'); together in modern English the compound means 'originating from Arabic' or 'borrowed from Arabic'.