The derivations of the $(2n+1)$-dimensional Heisenberg Lie Algebra have been determined, for example, here in Proposition $9$. The case $n=1$ has been computed at this site here:
Examples of derivation of Lie algebras
The derivations of the $(2n+1)$-dimensional Heisenberg Lie Algebra have been determined, for example, here in Proposition $9$. The case $n=1$ has been computed at this site here:
Examples of derivation of Lie algebras