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polyder

Polynomial Differentiation

q = polyder(p)

  • p should be a vector, real or complex, containing the coefficients of the polynomial $$ p(x)=p_1x^n+p_2x^{n-1}+\cdots+p_nx +p_{n+1}, $$ with p(1) being the highest order term.
  • q is contains the coefficients of the derivative $$ q(x)=\frac{d}{dx}p(x)=np_1x^{n-1}+(n-1)p_2x^{n-2}+\cdots+p_n. $$

q = polyder(a,b)

  • a and b should be vectors, real or complex, containing the coefficients of the polynomials a(x) and b(x), respectively.
  • q is the derivative of the product a(x)b(x), i.e., $$ q(x)=\frac{d}{dx}\left[a(x)b(x)\right]. $$

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

  • q and d represent the polynomials q(x) and d(x), which are, respectively, the numerator and denominator of the derivative $$ \frac{q(x)}{d(x)}=\frac{d}{dx}\left[\frac{a(x)}{b(x)}\right]. $$

Example 1: Differentiating x^4+2x^3+3x^2+4x+5 gives 4x^3+6x^2+6x+4.

polyder(1:5)
ans =
4.000   6.000   6.000   4.000

Example 2: The following two statments give the same results.

q1=polyder(1:5,1:2)
% Differentiation after polynomial multiplication using conv()
q2=polyder(conv(1:5,1:2))
q1 =
 5.000   16.00   21.00   20.00   13.00

q2 =
 5.000   16.00   21.00   20.00   13.00