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Derivations of universal enveloping algebra of Lie algebras

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.