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:

 

image\polyd01.gif

 

as the derivative of:

 

image\polyd02.gif

Example:

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

 

returns the series {2, 6} representing the polynomial:

 

image\polyd06.gif

 

as the derivative of:

 

image\polyd05.gif

Example:

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

 

returns the series {3, 8, 7} representing the polynomial:

 

image\polyd07.gif

 

as the derivative of the polynomial:

 

image\polyd08.gif

Example:

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

 

n == {1, 4, 1}

d == {1, 4, 4}

 

representing the polynomial:

 

image\polyd09.gif

 

as the derivative of:

 

image\polyd10.gif

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.

See Also:

CONV

DECONV

POLY

POLYFIT

POLYGRAPH

POLYINT

POLYVAL

ROOTS