# polylib::Dpoly

Differential operator for polynomials

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```polylib::Dpoly(`f`)
polylib::Dpoly(`indexlist`, `f`)
```

## Description

If `f` is a polynomial in the indeterminates `x1` through xn, `polylib::Dpoly([i1,..,ik], f)` computes the k-th partial derivative .

`polylib::Dpoly(f)` returns the derivative of `f` with respect to its only variable for an univariate polynomial `f`.

If some element of `indexlist` is greater than the number of indeterminates of `f`, the zero polynomial is returned.

`polylib::Dpoly([], p)` returns `p`.

If the coefficients of the polynomial are elements of a domain `d`, then this domain must have the method `"intmult"` (`d::intmult(e,i)`) that must calculate the integer multiple of a domain element `e` and a positive integer `i`.

## Examples

### Example 1

We differentiate a univariate polynomial with respect to its only indeterminate. In this case, we may leave out the first argument.

`polylib::Dpoly(poly(2*x^2 + x + 1));`

### Example 2

Now we differentiate a bivariate polynomial, and must specify the indeterminate in this case.

`polylib::Dpoly([1], poly(x^2*y + 3*x + y, [x, y]));`

### Example 3

It is also possible to compute second or higher partial derivatives.

`polylib::Dpoly([1, 2], poly(x^2*y + 3*x + y, [x, y]));`

## Parameters

 `f` Polynomial `indexlist` List of positive integers

## Return Values

`polylib::Dpoly` returns a polynomial in the same indeterminates and over the same coefficient ring as the input.

`f`