u'=2x,u ' ' = 2; When n≥3, u(n-order) =0 u(n-order) represents the n-order derivative of u, the same below.
V'= 1/( 1+x), when n≥2, v(n-order) = (-1) * n! /( 1+x)^n
F(n order) (x)=∑(k from 0 to n) c (n, k) u (n-k order) v(k order)
∴f(n order) (0)=C(n, n-2)*u(n-(n-2 order)) (0)*v(n-2 order) (0) +v(n order) In other words, the corresponding derivative of u is 0.
=n(n- 1)/2*2*(- 1)^(n-3)*(n-2)! /( 1 )^(n-2)+(- 1)^(n- 1)*n! /( 1)^n
=(- 1)^(n- 1)*(2n! )
That is, f(n order) (0) = (- 1) (n- 1) * (2n! ), where n≥3