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!_数学解答

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!

人气：353 ℃　时间：2020-03-27 18:37:47

解答

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...