The expression duly noted is a way of saying that something is “officially recognized” or “understood in full.”
In its most neutral use, duly noted is a way of saying “noticed and worth mentioning.” This use is often official or bureaucratic in tone.
Her fashion sense was duly noted by all.
The fact that you volunteered for the assignment is duly noted.
It’s often used to make it known that something that has been said or done by another person goes against the desire or decision of the speaker:
Your disagreement is duly noted.
Their complaints were duly noted but not appreciated.
Sometimes using duly noted shows that information is provided out of obligation or a kind of formal duty rather than enthusiasm; this can give a slightly negative or sarcastic tone to the sentence, making the “noted” elements seem unimportant or unremarkable.
We duly noted this third request for executive board action.
The fact that you paid for dinner this time is duly noted.
Duly is the adverb formed from due, meaning “owed” (“She is due two weeks’ pay;” “where credit is due”) or “appropriate” (“with all due respect”).
Synonyms of duly include properly and appropriately.