polyder

Polynomial differentiation

Syntax

k = polyder(p)
k = polyder(a,b)
[q,d] = polyder(a,b)

Description

example

k = polyder(p) returns the derivative of the polynomial represented by the coefficients in p,

k(x)=ddxp(x).

example

k = polyder(a,b) returns the derivative of the product of the polynomials a and b,

k(x)=ddx[a(x)b(x)].

example

[q,d] = polyder(a,b) returns the derivative of the quotient of the polynomials a and b,

q(x)d(x)=ddx[a(x)b(x)].

Examples

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Create a vector to represent the polynomial p(x)=3x5-2x3+x+5.

p = [3 0 -2 0 1 5];

Use polyder to differentiate the polynomial. The result is q(x)=15x4-6x2+1.

q = polyder(p)
q = 1×5

    15     0    -6     0     1

Create two vectors to represent the polynomials a(x)=x4-2x3+11 and b(x)=x2-10x+15.

a = [1 -2 0 0 11];
b = [1 -10 15];

Use polyder to calculate

q(x)=ddx[a(x)b(x)].

q = polyder(a,b)
q = 1×6

     6   -60   140   -90    22  -110

The result is

q(x)=6x5-60x4+140x3-90x2+22x-110.

Create two vectors to represent the polynomials in the quotient,

x4-3x2-1x+4.

p = [1 0 -3 0 -1];
v = [1 4];

Use polyder with two output arguments to calculate

q(x)d(x)=ddx[p(x)v(x)].

[q,d] = polyder(p,v)
q = 1×5

     3    16    -3   -24     1

d = 1×3

     1     8    16

The result is

q(x)d(x)=3x4+16x3-3x2-24x+1x2+8x+16.

Input Arguments

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Polynomial coefficients, specified as a vector. For example, the vector [1 0 1] represents the polynomial x2+1, and the vector [3.13 -2.21 5.99] represents the polynomial 3.13x22.21x+5.99.

For more information, see Create and Evaluate Polynomials.

Data Types: single | double
Complex Number Support: Yes

Polynomial coefficients, specified as two separate arguments of row vectors.

For more information, see Create and Evaluate Polynomials.

Example: polyder([1 0 -1],[10 2])

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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Differentiated polynomial coefficients, returned as a row vector.

Numerator polynomial, returned as a row vector.

Denominator polynomial, returned as a row vector.

Extended Capabilities

Introduced before R2006a