f(x)的导数=limx1->0[f(x+x1)-f(x)]/x1=limx1->0[ln(x+x1)-lnx]/x1=limx1->0[ln(1+x1/x)]/x1=limx1->0 1/x *x/x1 *ln(1+x1/x=1/x* limx1->0 ln(1+x1/x)^x/x1=1/x *lne=1/x