Write a program to do symbolic differentiation. Use the following formulas: Rule 1: (fg'-f+f'g Rule 2: (f+9)'-f+ Rule 3: ( g-s Rule 4: (ar") na"-1 An example of application of these rules is given below for differentiation with respect to x: 10z2y+100 (1(0)'by Rule 2 5+(-102)' by Rule 4 15102)' by Rule 3 15a(-10 v)' by Rule 4 26y 152,2 + (-10z?) y, + (-10r),y by Rule 1 15a20zy by Rule 4 First, run your program for polynomials only, and then add formulas for derivatives for trigonometric functions, logarithms, and so on, that extend the range of functions handled by your program. Write a program to do symbolic differentiation. Use the following formulas: Rule 1: (fg'-f+f'g Rule 2: (f+9)'-f+ Rule 3: ( g-s Rule 4: (ar") na"-1 An example of application of these rules is given below for differentiation with respect to x: 10z2y+100 (1(0)'by Rule 2 5+(-102)' by Rule 4 15102)' by Rule 3 15a(-10 v)' by Rule 4 26y 152,2 + (-10z?) y, + (-10r),y by Rule 1 15a20zy by Rule 4 First, run your program for polynomials only, and then add formulas for derivatives for trigonometric functions, logarithms, and so on, that extend the range of functions handled by your program