f = x' + mx + 7y
SymbolicDerivative[f,x] = x'' + mx'

f=Dt[x]+m x+7 y
Dt[f] /. {Dt[m] -> 0, Dt[y] -> 0}
(* output -> m Dt[x] + Dt[Dt[x]] *)

symD[f_, x_] := Module[{y, r},
r = Dt[f];
y = #[[1 ;; -2]] & /@ Position[r, Dt];
y = Part[r, Sequence @@ #] & /@ y;
y = DeleteDuplicates[Pick[y, Length[#] == 1 & /@ Dimensions /@ y]];
y = Select[y, Not[#[[1]] === x] &];
y = # -> 0 & /@ y;
r /. y]