We have known many derivations of Lie algebra. However, for the universal enveloping algebra of Lie algebra, we have little references about it. My question: The derivations of enveloping algebra is very hard or easy  ? Since for the one-dimensional Lie algebra, all its derivations form the one-sided Witt algebra. And does their some applications about it.

We know a lot about derivations of Lie algebra. However, for the universal enveloping algebra of Lie algebra, we have few references about it. My question: describing the derivations of enveloping algebras is very hard or easy? And are there any applications about it?

For example, for the one-dimensional Lie algebra, the derivations of the universal enveloping algebra form the one-sided Witt algebra.