polyder

Polynomial differentiation

Syntax

k = polyder(p)

k = polyder(a,b)

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

Description

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

$$k\left(x\right)=\frac{d}{dx}p\left(x\right).$$

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

$$k\left(x\right)=\frac{d}{dx}\left[a\left(x\right)b\left(x\right)\right].$$

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

$$\frac{q\left(x\right)}{d\left(x\right)}=\frac{d}{dx}\left[\frac{a\left(x\right)}{b\left(x\right)}\right].$$

Examples

Differentiate Polynomial

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

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

Use polyder to differentiate the polynomial. The result is $$q(x)=15x^4-6x^2+1$$.

q = polyder(p)

q = 1×5

    15     0    -6     0     1

Differentiate Product of Polynomials

Create two vectors to represent the polynomials $$a(x)=x^4-2x^3+11$$ and $$b(x)=x^2-10x+15$$.

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

Use polyder to calculate

$$q(x)=\frac{d}{dx}[a(x)b(x)].$$

q = polyder(a,b)

q = 1×6

     6   -60   140   -90    22  -110

The result is

$$q(x)=6x^5-60x^4+140x^3-90x^2+22x-110.$$

Differentiate Quotient of Polynomials

Create two vectors to represent the polynomials in the quotient,

$$\frac{x^4-3x^2-1}{x+4}.$$

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

Use polyder with two output arguments to calculate

$$\frac{q(x)}{d(x)}=\frac{d}{dx}\left[\frac{p(x)}{v(x)}\right].$$

[q,d] = polyder(p,v)

q = 1×5

     3    16    -3   -24     1

d = 1×3

     1     8    16

The result is

$$\frac{q(x)}{d(x)}=\frac{3x^4+16x^3-3x^2-24x+1}{x^2+8x+16}.$$

Input Arguments

p — Polynomial coefficients

vector

Polynomial coefficients, specified as a vector. For example, the vector [1 0 1] represents the polynomial $$x^2+1$$, and the vector [3.13 -2.21 5.99] represents the polynomial $$3.13x^2-2.21x+5.99$$.

For more information, see Create and Evaluate Polynomials.

Data Types: single | double
Complex Number Support: Yes

a,b — Polynomial coefficients (as separate arguments)

row vectors

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

k — Differentiated polynomial coefficients

row vector

Differentiated polynomial coefficients, returned as a row vector.

q — Numerator polynomial

row vector

Numerator polynomial, returned as a row vector.

d — Denominator polynomial

row vector

Denominator polynomial, returned as a row vector.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The output can contain fewer NaNs than the MATLAB^® output. However, if the input contains a NaN, the output contains at least one NaN.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The polyder function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a