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Integrate and Differentiate Polynomials

This example shows how to use the polyint and polyder functions to analytically integrate or differentiate any polynomial represented by a vector of coefficients.

Use polyder to obtain the derivative of the polynomial p(x)=x3-2x-5. The resulting polynomial is q(x)=ddxp(x)=3x2-2.

p = [1 0 -2 -5];
q = polyder(p)
q = 1×3

     3     0    -2

Similarly, use polyint to integrate the polynomial p(x)=4x3-3x2+1. The resulting polynomial is q(x)=p(x)dx=x4-x3+x.

p = [4 -3 0 1];
q = polyint(p)
q = 1×5

     1    -1     0     1     0

polyder also computes the derivative of the product or quotient of two polynomials. For example, create two vectors to represent the polynomials a(x)=x2+3x+5 and b(x)=2x2+4x+6.

a = [1 3 5];
b = [2 4 6];

Calculate the derivative ddx[a(x)b(x)] by calling polyder with a single output argument.

c = polyder(a,b)
c = 1×4

     8    30    56    38

Calculate the derivative ddx[a(x)b(x)] by calling polyder with two output arguments. The resulting polynomial is

ddx[a(x)b(x)]=-2x2-8x-24x4+16x3+40x2+48x+36=q(x)d(x).

[q,d] = polyder(a,b)
q = 1×3

    -2    -8    -2

d = 1×5

     4    16    40    48    36

See Also

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