f(x)=(x-1)*(x-2)*(x-3)*(x-2013)******(x-2014)求f*(2014)=?

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f(x)=(x-1)*(x-2)*(x-3)*(x-2013)******(x-2014)求f*(2014)=?

f(x)=(x-1)*(x-2)*(x-3)*(x-2013)******(x-2014)求f*(2014)=?
f(x)=(x-1)*(x-2)*(x-3)*(x-2013)******(x-2014)
求f*(2014)=?

f(x)=(x-1)*(x-2)*(x-3)*(x-2013)******(x-2014)求f*(2014)=?
f'(x)=(x-1)'*(x-2)*(x-3)*(x-2013)(x-2013)
除了最后一项,都有x-2014,则x=2014时为0
所以
f'(2014)=2013*2012*……*2*1=2014!

不妨设g(x)=(x-1)......(x-2013)
则f(x)=g(x)(x-2014)
f'(x)=g(x)+g'(x)(x-2014)
则f'(2014)=g(2014)+0=2013*2012*......*2*1=2013!(2013的阶乘)