### 28.4 Derivatives / Integrals / Transforms ¶

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

`k =` polyder `(p)` ¶
`k =` polyder `(a, b)` ¶
`[q, d] =` polyder `(b, a)` ¶

  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.

`q =` polyint `(p)` ¶
`q =` polyint `(p, k)` ¶

  Return the coefficients of the integral of the polynomial whose coefficients are represented by the vector p.

  The variable k is the constant of integration, which by default is set to zero.

  See also: polyder, polyval.

`g =` polyaffine `(f, mu)` ¶

  Return the coefficients of the polynomial vector f after an affine transformation.

  If f is the vector representing the polynomial f(x), then `g = polyaffine (f, mu)` is the vector representing:

      g(x) = f( (x - mu(1)) / mu(2) )

  See also: polyval, polyfit.