Kate's visit on Tuesday came as Universities UK, which represents 139 institutions including the University of Derby, published a new checklist to help them support student wellbeing during the autumn term.
The guide states that universities should ensure students have access to basic necessities during self-isolation, including food, laundry services, cleaning materials, bin bags, tissues and toilet rolls.
A surge in Covid-19 cases in recent weeks has led to thousands of students having to self-isolate in their halls at some universities, with some hanging signs out their windows saying they did not have food.
Nearly 500 students and staff at Sheffield University have tested positive for the virus since the start of term, and more than 750 students are self-isolating at Northumbria University after testing positive.
The National Union of Students (NUS) has warned that undergraduates being “trapped in halls” could exacerbate mental health issues.
Kate also travelled to the city to meet students and find out how their mental health is being cared for on campus.
Her visit to the university’s main Kedleston Road site ties in with World Mental Health Day on Saturday.
She was briefed by Student Minds, the UK’s student mental health charity, on the national picture and had her first discussion in a socially distanced circle.
Kate asked representatives of Student Minds if there had been an “increase in awareness” among students of mental health help – and asked if it had been “integrated” into their education.
Husna Hanif and Laura Oliver, both 18, told the duchess they had “kept busy” during lockdown – adding that it was “hard not seeing friends”.
She asked the pair if there was enough support at the university – to which Ms Oliver replied: “There’s so much support.”
“That’s great to hear,” Kate said.
The duchess also heard about the charity's Student Space initiative, a new resource created to support students during the pandemic, which offers information and direct help by phone and text.
The 24/7 text service using trained volunteers is delivered in partnership with Shout, an initiative from the Royal Foundation’s Heads Together mental health campaign.
Kate was also told that nursing students have been buddied up with fellow students in the year above to provide them with peer support during challenging clinical placements, and that the university has trained its sports societies to enable students to support their teammates’ mental health.