函数f(x)有一阶导数,则limf(2+ln(t-1))/ln(t-1)=?

题目

函数f(x)有一阶导数,则limf(2+ln(t-1))/ln(t-1)=?

答案

直接用洛必达法则
lim[t->t0] f(2+ln(t-1))/ln(t-1)
=lim[t->t0] {f'(2+ln(t-1))*1/(t-1)}/{1/(t-1)}
=lim[t->t0] f'(2+ln(t-1))
=f'(2+ln(t0-1))