To function a function into a Maclaurin series, you need to differentiate it lots of times anyway, so making that into a Maclaurin series first won't help.

Differentiating it is easy enough though.

log_{e} [f(x)], when differentiated, becomes f'(x)/f(x)

Applying that here gives that d(log_{e} (1+x))/dx = 1/(1+x).

You'd then need to differentiate that again and again until you get as many terms as you need for your series.