Nilpotent derivation with divided Leibniz condition powers

Definition
A nilpotent derivation with divided Leibniz condition powers is a derivation with divided Leibniz condition powers $$d^{(i)}, i \in \mathbb{N}_0$$ such that there exists $$n$$ for which $$d^{(i)} = 0 \ \forall i \ge n$$. The smallest such $$n$$ is termed the nilpotency.

Note that because we aren't assuming that the derivation is actually a derivation with divided powers, it need not be the case that the derivation $$d^{(1)} = d$$ is a nilpotent derivation. However, if we wish, we can assume this condition separately.