The question concerns creating a function. Let consider the following code
With[{f = Function[t, Cos[t]]},
{First[#], f'[#]} &
]
which returns
(* ==> {First[#1], Function[t, Cos[t]]'[#1]} & *)
How to can I force it to return the derivative evaluated (only second part of the returned list); i.e., how to can I get
(* ==> {First[#1], -Sin[#1]} & *)
First@#
would be evaluated and you don't want that. So, you want to inject code into a held expression. Search for that in the site. $\endgroup$