Question

f(x)=ln[(e^(mx))+n] if m and n are constants, how would i find f'(x)= ?

Answer 1

m/(e^(mx))+n

Answer 2

the general rule is
\[\frac{d}{dx}\ln(F(x))= \frac{F'(x)}{F(x)}\]
now set \[u=e^{mx}+n\]
\[u'=me^{mx}\]
so the answer for \[\frac{d}{dx}\ln(u))= \frac{u'}{u}\]
which expands to \[\frac{me^{mx}}{e^{mx}+n}\]