设当x不等于0时,函数f(x)=[ln(1-x)]/x；当x=0时,f(x)=-1,若函数在点x=0处可导,求x=0时函数的导数值
问题描述：
设当x不等于0时,函数f(x)=[ln(1-x)]/x；当x=0时,f(x)=-1,若函数在点x=0处可导,求x=0时函数的导数值
答
f'(0)=lim(x →0) [f(x)-f(0)] / x
=lim [ln(1-x) / x +1] / x
=lim [ln(1-x) +x] / x^2 罗比达法则
=lim [1/(x-1) +1] / 2x
=lim 1/[2(x-1)]
=-1/2