函数 f(x)=(x-1)(x-2)(x-3)...(x-2007) 则f'(2007)=?

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函数 f(x)=(x-1)(x-2)(x-3)...(x-2007) 则f'(2007)=?

函数 f(x)=(x-1)(x-2)(x-3)...(x-2007) 则f'(2007)=?
函数 f(x)=(x-1)(x-2)(x-3)...(x-2007) 则f'(2007)=?

函数 f(x)=(x-1)(x-2)(x-3)...(x-2007) 则f'(2007)=?
f(x)=(x-1)(x-2)(x-3)...(x-2007)
f'(x)=(x-2)(x-3)...(x-2007) +(x-1)(x-3)...(x-2007)+
(x-1)(x-2)(x-4)...(x-2007)+.+(x-1)(x-2).(x-2006)
所以f'(2007)=(2007-2)(2007-3).(2007-2007)+(2007-1)(2007-3)...(2007-2007)+...+(2007-1)(2007-2)...(2007-2006)
=2006*2005*2004...*1
=2006!