No, None of $AC \rightarrow D$ and $BD \rightarrow E $ is a Partial dependency.
Partial Dependency :
If a non-prime attribute of the relation is getting derived by only a part of the composite candidate key then such dependency is defined as partial dependency.
Since, $AB$ is the Candidate key here, So, To have Partial dependency in this Relation $A$ only Or $B$ only should have derived any of $C,D,E$. Which is Not the case here.
The Given FD's are Transitive Dependencies :
Transitive Dependency
In Simple words, If a non-prime attribute of the relation is getting derived Transitively by Candidate key(s). So, A Partial Dependency is Also a Transitive dependency. In some sense a partial dependency is a special case of a transitive dependency.
If a non-prime attribute of the relation is getting derived by either another non-prime attribute or by the combination of part of the candidate key along with a non-prime attribute or by a Part of Candidate key then such dependency would be defined as transitive dependency.
Here, in the given relation, the combination of part of the candidate key along with a non-prime attribute is deriving Non-key attribute.
$AC \rightarrow D$ ...Where $A$ is Part of Candidate key and $C,D$ are Non-key attributes.
and $BD \rightarrow E $... Where $B$ is Part of Candidate key and $D,E$ are Non-key attributes.
NOTE that In some sense a partial dependency is a special case of a transitive dependency. On the other hand there are transitive dependencies that are not caused by partial dependencies.