# Documentation

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# polyder

Polynomial differentiation

## Syntax

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

## Description

example

k = polyder(p) returns the derivative of the polynomial represented by the coefficients in p,$k\left(x\right)=\frac{d}{dx}p\left(x\right)\text{\hspace{0.17em}}.$

example

k = polyder(a,b) returns the derivative of the product of the polynomials a and b,$k\left(x\right)=\frac{d}{dx}\left[a\left(x\right)b\left(x\right)\right]\text{\hspace{0.17em}}.$

example

[q,d] = polyder(a,b) returns the derivative of the quotient of the polynomials a and b,$\frac{q\left(x\right)}{d\left(x\right)}=\frac{d}{dx}\left[\frac{a\left(x\right)}{b\left(x\right)}\right]\text{\hspace{0.17em}}.$

## Examples

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### Differentiate Polynomial

Create a vector to represent the polynomial .

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

Use polyder to differentiate the polynomial. The result is .

q = polyder(p) 
q = 15 0 -6 0 1 

### Differentiate Product of Polynomials

Create two vectors to represent the polynomials and .

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

Use polyder to calculate

 
q = polyder(a,b) 
q = 6 -60 140 -90 22 -110 

The result is

 

### Differentiate Quotient of Polynomials

Create two vectors to represent the polynomials in the quotient,

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

Use polyder with two output arguments to calculate

 
[q,d] = polyder(p,v) 
q = 2 12 0 -11 d = 1 8 16 

The result is

 

## Input Arguments

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### p — Polynomial coefficientsvector

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 $3.13{x}^{2}-2.21x+5.99$.

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

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### k — Integrated polynomial coefficientsrow vector

Integrated polynomial coefficients, returned as a row vector.

### q — Numerator polynomialrow vector

Numerator polynomial, returned as a row vector.

### d — Denominator polynomialrow vector

Denominator polynomial, returned as a row vector.