设 f(x)=(x-1)(x-2)(x-3)…(x-2011),求f'(2011).求详解RT,期中复习看到错题...发现当时没有详解,答案是f'(2011)=2010!

设 f(x)=(x-1)(x-2)(x-3)…(x-2011),求f'(2011).求详解RT,期中复习看到错题...发现当时没有详解,答案是f'(2011)=2010!
设 f(x)=(x-1)(x-2)(x-3)…(x-2011),求f'(2011).求详解
RT,期中复习看到错题...发现当时没有详解,
答案是f'(2011)=2010!

设 f(x)=(x-1)(x-2)(x-3)…(x-2011),求f'(2011).求详解RT,期中复习看到错题...发现当时没有详解,答案是f'(2011)=2010!
f'(x)=(x-1)'*(x-2)(x-3)…(x-2011)+(x-1)(x-2)'*(x-3)…(x-2011)+……+(x-1)(x-2)(x-3)…(x-2011)‘
=(x-2)(x-3)…(x-2011)+(x-1)(x-3)…(x-2011)+……+(x-1)(x-2)(x-3)…(x-2010)
除了最后一项,都有x-2011
则x=2011时为0’
所以f'(2011)=2010*2009*2008*……*1=2010!