Mathematical function parameters

Yes, commercial programs of that complexity take several man-years to develop.

The .NET Framework only has basic mathematical support.

There's the static methods in the System.Math class:

http://msdn.microsoft.com/en-us/library/system.math.aspx 

and there's also the BigInteger and Complex types in the System.Numerics namespace:

http://msdn.microsoft.com/en-us/library/system.numerics.aspx 

Other than that you're more or less on your own though there are some third party libraries available if you google for them.

What I've done above should be able to differentiate any polynomial so I'd just use that and use a similar approach to integrate it.

    static void Main(string[] args)

    {      

        string input;

        string[] numbers;

        double[] terms; 

        bool isValid = false;

        double x; 

  

        do

        {  

           Console.WriteLine("Enter the terms of the polynomial, separated by spaces, highest degree first");

           input = Console.ReadLine().Trim();

           if (input == "") input = "a"; // to force an error message

           numbers = input.Split(new char[]{' '}, StringSplitOptions.RemoveEmptyEntries);

           terms = new double[numbers.Length];

           for (int i = 0; i < terms.Length; i++)

           {

              isValid = double.TryParse(numbers[i], out terms[i]);

              if (!isValid)

              {

                  Console.WriteLine("Terms must be numeric\n");

                  break;

              }

           }

        

        }

        while(!isValid);

        do

        {

           Console.WriteLine("Enter the value of x");

           input = Console.ReadLine(); 

           isValid = double.TryParse(input, out x);

           if(!isValid) Console.WriteLine("The value of x must be numeric\n");

        }

        while(!isValid);

           

        Polynomial poly = new Polynomial(terms);

        Polynomial poly2 = poly.Differentiate();

        Console.WriteLine("\nThe derivative of {0} is {1}", poly, poly2);

        Console.WriteLine("The value of the derivative when x is {0} is {1}", x, poly2.Evaluate(x));

        Console.ReadKey();

    }

The program differentiates (or 'cuts' as you call it) any polynomial passed to it.

It would not be difficult to add methods to integrate the polynomial and to evaluate the integral between two limits. You could also add a method to calculate maxima and minima provided the degree of the polynomial was not more than 3 though you might need the assistance of my article on solving quadratic equations using C# to find the stationary points of a third degree polynomial.

http://www.c-sharpcorner.com/uploadfile/b942f9/using-the-complex-type-to-solve-quadratic-equations/ 

However, you would of course need additional methods to deal with trigonometric functions, transcendental functions, functions involving two or more variables etc. You'd also need a way of distinguishing between the various types of function that the user might input.

So to do all this would involve a considerable amount of work and I wouldn't expect to finish any time soon.

Here's a program I wrote some time ago which includes a rudimentary polynomial class plus methods to differentiate, evaluate and display it. 

The program accepts its arguments from the command line. So, if you wanted to differentiate x^3 + 2x^2 + 3x + 4, you'd type in:

    polycalc 1 2 3 4

or, if you wanted to differentiate x^3 - 3x + 4, you'd type in:

    polycalc 1 0 -3 4

because there's no x^2 term.

For now, it just illustrates evaluation by always using a value of 2 for x though it could, of course, be easily altered to accept the value as an additional argument or to ask the user to input it: