  Given a result of Herman, we provide a new elementary proof of the fact that
the connected component of the group of compactly supported diffeomorphisms is
perfect and hence simple. Moreover, we show that every diffeomorphism $g$,
which is sufficiently close to the identity, can be represented as a product of
four commutators, $g=[h_1,k_1]\circ...\circ[h_4,k_4]$, where the factors $h_i$
and $k_i$ can be chosen to depend smoothly on $g$.
