Write a program to do symbolic differentiation. Use the following formulas:

An example of the application of these rules is given below for differentiation with respect to x:

The program is supposed to be written in c++, using a switch statement that detects which case needs to be used to implement each rule. And the functions need to be written using recursion in some form.

Rule 1: (g-g' +f'g Rule 3: (f),=f's_fe f'g -fg e 5: - Rule 4: (ax"), = nar- (se+,-10-y + 100) (5ry. + (-meyr . (oor 6x (-10'y)+(100 by Rule 2 by Rule 4 by Rule 3 by Rule 4 by Rule 1 by Rule 4 - 15x2+ (-10xy) 6y 520xy