The derivative defines the limit of (f(x+△x)- f(x))/△x at △x=0, so ln(x).

Lim (△ x→ 0) (ln (x+△ x)-ln (x))/△ x =1/x How to get this limit is beyond the knowledge of senior high school. It is enough for high school to know (ln (x))' =1/x.