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)=______.
答
由于f′(2013)=
lim x→2013
f(x)−f(2013) x−2013
=
lim x→2013
(x−1)(x−2)…(x−2013) x−2013
=
(x−1)(x−2)…(x−2012)lim x→2013
=2012!