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

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

若函数f(x)=(x-1)(x-2)(x-3)...(x-2007)函数 f(x)=(x-1)(x-2)(x-3)...(x-2007) 则f'(2007)=?
f(x)=g(x)(x-2007)
f'(x)=g'(x)(x-2007)+g'(x)
g(x)=(x-1)..(x-2006)
g'(x)=g(x)/(x-1)+..g(x)/(x-2006)
f'(2007)=g'(2007)=g(2007)[1/2006+1/2005+..+1/1]=2006![1/2006+1/2005+..+1/1]

f(x)=(x-1)(x-2)(x-3)...(x-2007)
令：g(x) = (x-1)(x-2)(x-3)...(x-2006)
f(x) = g(x) (x-2007)
f '(x) = g'(x) (x-2007) + g(x) //: (uv)'=u'v+uv'
f '(2007) = ...

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f(x)=(x-1)(x-2)(x-3)...(x-2007)
令：g(x) = (x-1)(x-2)(x-3)...(x-2006)
f(x) = g(x) (x-2007)
f '(x) = g'(x) (x-2007) + g(x) //: (uv)'=u'v+uv'
f '(2007) = g'(2007)(2007-2007) + g(2007)
f '(2007) = 0 + (2007-1)(2007-2)(2007-3)...(2007-2006)
= 1×2×3×.....×2006
f '(2007) = 2006!

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