A new hospital in Derby is seeking $3 million in loan guarantees from Sedgwick County and the city of Derby to try to right itself financially amid the coronavirus pandemic, according to hospital and county officials. With finances stressed by delays in setting up government health care payments — and then depressed patient counts due to the threat of COVID-19 — Rock Regional Hospital is asking the county and Derby to act as guarantors for $3 million of a $5 million bank loan the hospital is applying for, officials said.