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### 27.4 Derivatives / Integrals / Transforms

Octave comes with functions for computing the derivative and the integral of a polynomial. The functions `polyderiv` 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

— Function File: polyderiv (p)
— Function File: [k] = polyderiv (a, b)
— Function File: [q, d] = polyderiv (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: poly, polyint, polyreduce, roots, conv, deconv, residue, filter, polygcd, polyval, polyvalm.

— Function File: polyderiv (p)
— Function File: [k] = polyderiv (a, b)
— Function File: [q, d] = polyderiv (b, a)

> An alias for `polyderiv`.

> See also: polyderiv.

— Function File: polyint (p)
— Function File: 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: poly, polyderiv, polyreduce, roots, conv, deconv, residue, filter, polyval, polyvalm.

— Function File: 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.