Hi
As Thomas Rose Snr in the 1881 Census is living in Whittington, Derbyshire
and gives his birth as 1834 I think it safe to assume that the Death
in the Chesterfield Registration District in 1882 for a Thomas Rose aged 48
is the same Thomas Rose, as Whittington comes within the Chesterfield
Registration District. To be certain you would need the Death Certificate
in the hope that the person reporting the Death was Thomas Rose Jnr
also living at the same address per 1881 Census.
For an additional check:-
You also need to search Nottinghamshire 1881 Census for the Thomas
Rose who died in 1881 aged 56, note this death was for Newark Registration
District so DO NOT restrict your search to just Newark.
When you have done this - which do you think is your Thomas Rose Snr?
Spendlove