'unproblematically' originates from the prefix 'un-' meaning 'not' and the word 'problematic,' which comes from the Greek word 'problematikos,' meaning 'pertaining to a problem.'

'Problematikos' transformed into the Latin word 'problematicus,' and eventually became the modern English word 'problematic,' with 'un-' added to form 'unproblematic' and then 'unproblematically.'

Initially, it meant 'not pertaining to a problem,' but over time it evolved into its current meaning of 'free from problems or difficulties.'