differentiate a polynomial in csharp

To differentiate a polynomial in c#, you can use various methods such as the forward or backward difference method, central difference method, or use a standard formula like the power rule or product rule. Here is an example code using the power rule to differentiate a polynomial:

main.cs
public static double[] Differentiate(double[] coefficients)
{
   int degree = coefficients.Length - 1;
   double[] result = new double[degree];

   for (int i = degree; i > 0; i--)
   {
      result[degree - i] = i * coefficients[degree - i];
   }

   return result;
}
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In this method, the input is an array of coefficients of a polynomial, in decreasing order of degree (e.g., the first element is the coefficient of the highest-degree term). The method then calculates the derivative of the polynomial using the power rule and returns an array with the coefficients of the resulting polynomial.

For example, if the input array is { 3, 2, 1 } (which represents the polynomial 3x^2 + 2x + 1), the method will return an array with the coefficients of the derivative, which is { 6, 2 } (representing 6x + 2).