lim(x->∝)ln(x+e^x) /x =lim(x->∝)(1+e^x)/(x+e^x)

题目

lim(x->∝)ln(x+e^x) /x =lim(x->∝)(1+e^x)/(x+e^x)
这一步是怎么得来的呀?看不懂,求教

答案

无穷/无穷 等式上下分别求导
=lim 1/(x+e^x)*(x+e^x)'/x'
=lim 1/(x+e^x)*(1+e^x)
=lim (1+e^x)/(x+e^x)