dist = NormalDistribution[\[Mu][\[Alpha]], \[Delta][\[Alpha]]]; f =
 PDF[dist, x]; h = FullSimplify[Dt[Log[f], {\[Alpha], 2}]];
h = FullSimplify[h //. {Dt[x, _] :> 0}];
fim = Expectation[-h, x \[Distributed] dist]