IPA: /ʌnˈpɜːrsweɪzɪvli/
KK: /ʌnˈpɜr.sweɪ.zɪv.li/
In a manner that does not convince or influence someone.
She presented her argument unpersuasively, failing to change anyone's mind.
Unpersuasively → It is formed from "un-" (meaning not), "persuade" (from Latin "persuadere", meaning to convince or persuade), and "-ly" (meaning in a manner). The word "unpersuasively" means in a manner that does not convince or persuade.
Think of 'not' ('un-') convincing someone ('persuade') — that's why unpersuasively means not convincing.