diff (ln (t)/(1-t),t)

-log(t)/(t - 1)

diff(log(t)/(-t + 1), t)

solve(log(t)/(-t + 1), t)

series(log(t)/(-t + 1), t, 0, 10)

Want to compute something more complicated? Try a full Python/SymPy console at SymPy Live.