Persuasive

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late 15th century: from French persuasif, -ive or medieval Latin persuasivus, from persuas- ‘convinced by reasoning’, from the verb persuadere (see persuade).

wiktionary

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From Middle French persuasif, from Medieval Latin persuāsīvus, from Latin past participle stem of persuādēre + -īvus

etymonline

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persuasive (adj.)

"having the power of persuading," 1580s, from French persuasif, from Medieval Latin persuasivus, from Latin persuas-, past-participle stem of persuadere "persuade, convince" (see persuasion). Related: Persuasively; persuasiveness. Replaced earlier persuasible in this sense (see persuadable).