With the initialization cells from SynergeticsCoordinatesDemo.nb (600.8 KB) - Mathematica Notebook
http : // library.wolfram.com/infocenter/MathSource/600/
Clear[f, a, b, c, d]
f[x_] := a x^3 + b x^2 + c x + d
r5 = rootOfUnity[5]
B[1, 1, 1, -4, 1]
df[x_] := Sum[(f[x + r5^p] - f[x - r5^p])/r5^p, {p, 1, 5}]/2/5
D[f[x], x]
c + 2 b x + 3 a x^2
Expand[df[x]] /. B[0, 0, 0, 0, 0] -> 0
c B[1, 1, 1, 1, -4] + b x B[2, 2, 2, 2, -8] + a x^2 B[3, 3, 3, 3, -12]
You use a different version of Mathematica than I do. Check the derivative of f[x].