设f(x)=x*(x-1)*(x-2)……(x-2009),则f'(0)=

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设f(x)=x*(x-1)*(x-2)……(x-2009),则f'(0)=

f(0)=0
所以:
f'(0)=lim[f(x)-f(0)]/(x-0)
=lim[x*(x-1)*(x-2)……(x-2009)]/x
=lim(x-1)*(x-2)……(x-2009)
=(-1)(-2)...(-2009)
=-2009!