#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 Ln : public Expression {  //защищенный член класса доступен только методам этого класса и всех производных от него классов.
protected:
	Expression* x;

public:
	Ln(Expression* v) : x(v) {}
	Expression* diff() { return new Div(new Number(1), x); }
	void print() {
		cout << "ln(";
		x->print();
		cout << ')';
	}
};

class Log : public Ln {
	double a;

public:
	Log(double n, Expression* v) : a(n), Ln(v) {}
	Expression* diff() {
		return new Div(new Number(1), new Mul(x, new Ln(new Number(a))));
	}
	void print() {
		cout << "log_" << a << '(';
		x->print();
		cout << ')';
	}
};

int main() {
	//Expression* e = new Log(3, new Add(new Number(1), new Variable('x')));
	Expression *e = new Add(new Number('x'), new Variable('x'));
	Expression* de = e->diff();
	e->print();
	cout << "\n";
	de->print();
	cout << "\n";
	delete e;
	delete de;
	system("pause");
}