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_数学解答

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!

人气：224 ℃　时间：2020-06-10 08:25:05

解答

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...