How about this:

Code:(* Create table of {{vn,in}} test values *) mytable = Table[{n, n}, {n, 1, 10}] (* switch the {v,i) to {log[i],v} *) newtable = {N[Log[#[[2]]]], #[[1]]} & /@ mytable (* calculate interpolation function of the list {log (i),v} *) myfunction = Interpolation[newtable] (* calculate the derivative dv/d log (i) *) mydev[t_] = D[myfunction[t], t] Plot[mydev[t], {t, 1, 10}]