In[]:=
$Version
Out[]=
14.2.0 for Microsoft Windows (64-bit) (December 26, 2024)
In[]:=
d[v_]:=HankelH1[v,k1b]+HankelH2[v,k1b];
In[]:=
F[k1_,b_,v_]:=Evaluate[D[d[v],v]//FunctionExpand];
In[]:=
F[1,2,1/2]//N,F[1,2,1/2+2I]//N,F[1-I,2+1/2I,1/2-2I]//N,F1-I,3,-2-//N
I
2
Out[]=
{0.68095,-9.26329-5.78201,0.117177+1.40826,-0.666794-4.14499}