數學M2:first principle

dy/dx
=lim(h->0) [ln(x+h)-lnx]/h
=lim(h->0) [ln(1+h/x)]/h
=lim(t->0) [ln(1+t)]/(tx) where t=h/x
=lim(t->0) [ln(1+t)^(1/t)]/x
=1/x (ln e) as (lim t->0 (1+t)^(1/t)=e)
=1/x

You have to make use of the relation : e^x = lim (1 + hx)^(1/h) h tends to zero. Is this in the M2 syllabus?