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)=______.
答
∵f′(0)=
lim x→0
=f(x)−f(0) x
lim x→0
x(x+1)…(x+n) x
(x+1)…(x+n)=n!lim x→0