F(x)=x(x-1)(x-2)(x-3)………(x-100),求F(1)的导数.具体点,麻烦你你们了!

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/05/16 04:40:53

两边求对数
lnF(x)=ln(x(x-1)(x-2)(x-3)………(x-100))
=lnx+ln(x-1)+...+ln(x-100)
两边求导
F'(x)/F(x)=1/x+1/(x-1)+...+1/(x-100)
F'(x)=(1/x+1/(x-1)+...+1/(x-100))F(x)
=(x-1)(x-2)(x-3)...(x-100)+x(x-2)(x-3)...(x-100)+...
只有第二项不含x-1
所以是F'(1)=1(1-2)(1-3)...(1-100)=-99!

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