Write a C++ Function

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

Rule 1: ( f g ) ′ = f g ′ + f ′ g

Rule 2: ( f + g ) ′ = f ′ + g ′

Rule 3: ( f/ g ) ′ = (f ′ g − f g ′)/ g 2

Rule 4: ( ax^n )^-1 = nax^(n-1)

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

Literally follow this example.

( 5^3 + 6 xy − 10x^2 y + 100 )′

= ( 5x^3)' + (6x/y)'+(-10x^2y)'+(100)' by Rule 2

= 15 x^2 + (6 x /y)′ + (− 10 x^2 y )' +(100) ′ by Rule 4

= 15 x^2 + [(6 x)′y − (6x)y ′ ]/ y^2 + (−10x^2 y)′ by Rule 3

= 15 x^2 + 6y /y^2 + ( −10 x^2 y )′ by Rule 4

= 15 x^2 + 6 y/ y^2 + (−10 x^2) y ′ + (−10 x^2) ′ y by Rule 1

= 15x^2 + 6/y - 20xy by Rule 4

Then find the second derivative

Then 4th

etc.

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.

Algorithm C Programming Uprogramu C++ Software Architecture

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ManormaShehzadi

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