In case the definition is not standard, my book defines a derivation $D \in \text{End}(\mathfrak{g})$ of a Lie algebra $\mathfrak{g}$ as a linear map such that:
$D([X,Y]) = [D(X), Y]\ +\ [X, D(Y)]$ for all $X,Y \in \mathfrak{g}$
It is well-known that for two derivations $D$ and $D'$ of $\mathfrak{g}$, $[D, D'] = D \circ D'\ -\ D' \circ D$ is again a derivation of $\mathfrak{g}$.
However, the exercise asks for an example of a Lie algebra and two derivations such that the composition $D \circ D'$ is not a derivation. My idea was to take the Heisenberg Lie algebra, but I have been unable to find two derivations whose composition is not again a derivation. Am I missing something simple? I feel like this shouldn't be too hard.