#include <iostream>
#include <iomanip>
#include <vector>
#include <functional>
#include <cmath>

typedef long double Type;
constexpr Type eps = 1E-12;

using analysisFunction = std::function<const Type(const Type, const Type)>;

class derivatives {
    private:
        class derivative;
    public:
        derivatives(std::vector<analysisFunction>& p_fList) { fList = &p_fList; };
        derivative operator[](int index) {
            return derivative((*fList).at(index));
        }
    private:
        class derivative {
            public:
                derivative(analysisFunction& p_f) { f = &p_f; }
                Type operator()(Type t, Type u) {
                    return (((*f)(t, u + eps)) - ((*f)(t,u)))/eps;
                }
            private:
                analysisFunction *f;
        };
        std::vector<analysisFunction> *fList;
};

int main ()
{
    std::vector <analysisFunction> numericalFunctions;
    auto& f = numericalFunctions;

    f.push_back([](Type t, Type u)->Type { return u*u; });


    std::cout << std::setprecision(16);
    std::cout << f[0](5.0, 10.0) << '\n';

    derivatives dfdt(f);
    std::cout << dfdt[0](5.0, 10.0);
    return 0;
}