两边求对数
lnF(x)=ln(x(x-1)(x-2)(x-3)………(x-100))
=lnx+ln(x-1)+...+ln(x-100)
两边求导
F'(x)/F(x)=1/x+1/(x-1)+...+1/(x-100)
F'(x)=(1/x+1/(x-1)+...+1/(x-100))F(x)
=(x-1)(x-2)(x-3)...(x-100)+x(x-2)(x-3)...(x-100)+...
只有第二项不含x-1
所以是F'(1)=1(1-2)(1-3)...(1-100)=-99!