// innermost function
double g(double x, vector<double> pars){
  return x * pars[0] * pars[0];
}
// some intermediate function
template <typename F>
auto f0(F const & f, double x, vector<double> pars) {
   return [f, pars](double x, vector<double> pars) {
     vector<double> pars_0(pars);
     pars_0[0] = 0;
     return f(x, pars_0);
   };
}
// another intermediate function
template <typename F>
auto f1(F const & f, double x, vector<double> pars) {
   return [f, pars](double x, vector<double> pars) {
     vector<double> pars_1(pars);
     pars_1[0] = 1;
     return f(x, pars_1);
   };
}
// selector function
template <typename F>
auto D(F const & f, double x, vector<double> pars, int degree) {
  if(0 == degree) {
    return f0(f, x, pars)(x, pars);
  } else {
    return f1(f, x, pars)(x, pars);
  }
}

template <typename F>
auto D(F const & f, double x, vector<double> pars, int degree) {
  if(0 == degree) {
    return [f, x, pars](F const & f, int x, vector<double> pars) {
      return D(f0(f, x, pars)(x, pars)); // <<< ?
      };
  } else {
    return // same stuff for the other function(s)
  }
}

int sum = 0;
for(int i = 0; i < 3; ++i ){
    for(int j = 0; j < 3; ++j ){
        for(int k = 0; k < 3; ++k ){
            ...
            sum += D(...(D(g, i), j)...,k) (pars of the lambdas);
            // number of for loops depends on size of pars passed to f
        }
    }
}