Octave comes with functions for computing the derivative and the integral
of a polynomial.  The functions polyder and polyint
both return new polynomials describing the result.  As an example we'll
compute the definite integral of p(x) = x^2 + 1 from 0 to 3.
     c = [1, 0, 1];
     integral = polyint(c);
     area = polyval(integral, 3) - polyval(integral, 0)
     ⇒ 12
   
   Return the coefficients of the derivative of the polynomial whose coefficients are given by the vector p. If a pair of polynomials is given, return the derivative of the product a*b. If two inputs and two outputs are given, return the derivative of the polynomial quotient b/a. The quotient numerator is in q and the denominator in d.
See also: polyint, polyval, polyreduce.