令 g(x) = (x-1)(x-2)...........(x-100)
则 f(x) = xg(x)
由两函数相乘求导公式可知,f'(x) = g(x) + xg'(x)
x=0时,xg'(x)一项为0
所以 f'(0) = g(0) = (-1)(-2)...(-100) = 100!
(! 表示 阶乘)