设f(x)=(x-1)(x-2)…(x-2013),求f′(2013)=_.

问题描述:

设f(x)=(x-1)(x-2)…(x-2013),求f′(2013)=______.

由于f′(2013)=

lim
x→2013
f(x)−f(2013)
x−2013

=
lim
x→2013
(x−1)(x−2)…(x−2013)
x−2013

=
lim
x→2013
(x−1)(x−2)…(x−2012)

=2012!