“f(x)=(x--1)*(x-2)*(x-3).(x-100)当x=3时,求其导函数.

题目

“f(x)=(x--1)*(x-2)*(x-3).(x-100)当x=3时,求其导函数.

答案

ln|f(x)|=∑[1,100]ln|x-k|
f'(x)/f(x)=∑[1,100]1/(x-k)
f'(x)=f(x)∑[1,100]1/(x-k)
f'(3)=(x-1)(x-2)(x-4)...(x-100)
=2*(-1)^97*97!
=-2*97!