#include <iostream>
using namespace std;
class Expression
{
public:
    virtual Expression* diff() = 0;
    virtual void print() = 0;
};

class Number : public Expression
{
    double value;
public:
    Number(double x)
    {
        value = x;
    }
    Expression* diff()
    {
        return new Number(0);
    }
    void print()
    {
        cout << value;
    }
};

class Variable : public Expression
{
    char value;
public:
    Variable(char x)
    {
        value = x;
    }
    Expression* diff()
    {
        return new Number(1);
    }
    void print()
    {
        cout << value;
    }
};

class Add : public Expression
{
    Expression* left, * right;
public:
    Add(Expression* l, Expression* r)
    {
        left = l;
        right = r;
    }
    Expression* diff()
    {
        return new Add(left->diff(), right->diff());
    }
    void print()
    {
        cout << "(";
        left->print();
        cout << ")";
        cout << '+';
        cout << "(";
        right->print();
        cout << ")";
    }
};

class Sub : public Expression
{
    Expression* left, * right;
public:
    Sub(Expression* l, Expression* r)
    {
        left = l;
        right = r;
    }
    Expression* diff()
    {
        return new Sub(left->diff(), right->diff());
    }
    void print()
    {
        cout << "(";
        left->print();
        cout << ")";
        cout << '-';
        cout << "(";
        right->print();
        cout << ")";
    }
};

class Mul : public Expression
{
    Expression* left, * right;
public:
    Mul(Expression* l, Expression* r)
    {
        left = l;
        right = r;
    }
    Expression* diff()
    {
        return new Add(new Mul(left->diff(), right), new Mul(left, right->diff()) );
    }
    void print()
    {
        cout << "(";
        left->print();
        cout << ")";
        cout << '*';
        cout << "(";
        right->print();
        cout << ")";
    }
};

class Div : public Expression
{
    Expression* left, * right;
public:
    Div(Expression* l, Expression* r)
    {
        left = l;
        right = r;
    }
    Expression* diff()
    {
        return new Div(new Sub(new Mul(left->diff(), right), new Mul(left, right->diff())), new Mul(right, right));
    }
    void print()
    {
        cout << "(";
        left->print();
        cout << ")";
        cout << "/";
        cout << "(";
        right->print();
        cout << ")";
    }
};


class arctg : public Expression
{
    Expression* x;
public:
    arctg(Expression* v)
    {
        x = v;
    }
    Expression* diff()
    {
        return new Mul(x->diff(), new Div(new Number(1),new Add(new Number(1),new Mul(new Variable('x'), new Variable('x')))));
    }
    void print()
    {
        cout << "arctg" << '(';
        x->print();
        cout << ')';
    }
};


int main()
{
    Expression* e = new arctg(new Mul(new Number(2), new Variable('x')));
    Expression* de = e->diff();
    e->print();
    cout << "\n";
    de->print();
    cout << "\n";
    delete e;
    delete de;
    system("pause");
    return 0;
}