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### 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
```
Function File: polyder (p)
Function File: [k] = polyder (a, b)
Function File: [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.

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.

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) )