设f(x)=x(x+1)(x+2)…(x+n),则f′(0)=_.

问题描述:

设f(x)=x(x+1)(x+2)…(x+n),则f′(0)=______.

f′(0)=

lim
x→0
f(x)−f(0)
x
lim
x→0
x(x+1)…(x+n)
x
lim
x→0
(x+1)…(x+n)=n!