The US president arrived in the UK yesterday as part of a three-day state visit.
Thousands of people are expected to protest in London and similar events have been held across the country, including in Chesterfield.
Yesterday, Derbyshire Armed Response Unit tweeted: "Our specialist skills are on demand for the visit of @realDonaldTrump to the UK. This week we have let the Met borrow rifle and CP officers before some of our crews head down to @HantsPolice to assist with the President's visit to remember the anniversary of D-Day. #TrumpUKVisit."
But one person replied: "What a bizarre tweet! An open invitation to local criminals that Derbyshire now has even less resources available to them!"
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In response, Derbyshire Armed Response Unit wrote: "Our minimum staffing resources are not compromised, our staff are working cancelled rest days (remember there are no “extra police”) - so no harm to our day to day policing."
And a spokesperson for Derbyshire Constabulary said each police force is asked to supply officers to support large scale operations.
“We put forward a number of officers, with a variety of skills to assist with this operation," the spokesperson said.
“As stated in the response from the armed response unit – there has been no effect on the day-to-day operational policing of the county or of the safety of visitors to, and residents of, Derbyshire.
“A further key part of this national agreement when large scale operations or incidents occur in Derbyshire we are able to avail ourselves of officers from other forces to support our policing duties.”