# POLYDER

## Purpose:

Calculates the derivative of a polynomial.

## Syntax:

POLYDER(p, form)

r = POLYDER(p, q, form)

(n, d) = POLYDER(p, q, form)

p

-

A series, the coefficients of the source polynomial.

q

-

Optional. A series, the coefficients of a polynomial to multiply with p or divide into p depending on the number of the output arguments.

form

-

Optional. An integer, the polynomial coefficient form:

 0: ascending powers, lowest degree to highest 1: descending powers, highest degree to lowest (default)

## Returns:

A series, the resulting polynomial coefficients.

r = POLYDER(p) returns the polynomial coefficients of the derivative of p.

r = POLYDER(p, q) returns the polynomial coefficients of the derivative of p * q.

(n, d) = POLYDER(p, q) returns n the numerator and d the denominator polynomial coefficients of p / q.

## Example:

polyder({1, 2, 3})

returns the series {2, 2} representing the polynomial: as the derivative of: ## Example:

polyder({1, 2, 3}, 0)

returns the series {2, 6} representing the polynomial: as the derivative of: ## Example:

polyder({1, 2, 3}, {1, 2})

returns the series {3, 8, 7} representing the polynomial: as the derivative of the polynomial: ## Example:

(n, d) = polyder({1, 2, 3}, {1, 2})

n == {1, 4, 1}

d == {1, 4, 4}

representing the polynomial: as the derivative of: ## Example:

polyder(polyint({1, 2, 3}))

returns the series {1, 2, 3} indicating that POLYINT is an inverse function of POLYDER.

## Remarks:

If the input is a matrix, POLYDER considers each column to represent the polynomial coefficients with the result having the same number of columns as the input.

See POLYINT to perform polynomial integration.

CONV

DECONV

POLY

POLYFIT

POLYGRAPH

POLYINT

POLYVAL

ROOTS