How to use correctly \dl with vectors using the diffcoeff package?

For reasons that are unknown to me, the \dl command absorbs an argument. So your attempt

\dl \vec{x}

absorbs \vec as its argument and chaos ensues.

The implementation of \dl is very awkward. It comes out that

\dl 0 \vec{x}

works (spaces are optional).

Are you sure you want to use the package?