已知函数f(x)=x(x-1)(x-2)… (x-100),则f'(0)=

用求导的定义

已知:f(0)=0*(0-1)(0-2)……=0

............f(x)-f(0)......... x(x-1)… (x-100)
f'(0)=limit------------=limit---------------------
........x→0.......x-0.....x→0 ........ x

x约掉,0带入

=-1*-2*……*-100=100!

f(x)=x(x-1)(x-2)… (x-100)
＝x^101＋……+100!x
f(x)'=101x^100+……+?x+100!
f'(0)=100!

应该是-100!哈