Suppose we have a relation R(A,B,C,D,E) with candidate keys {A,B} , {C,D} and let E be a non prime attribute.
If there is a dependency C->E then it is partial dependency as E depends on a part of candidate key {C,D}
Is dependency BC->E partial?
A functional dependency is partial if, on removing one or more attributes from the determinant (left-hand side), you still have a dependency that holds. In your example therefore:
{C}→{E} is a full functional dependency
{C,D}→{E} is a partial functional dependency because {C}→{E}
{B,C}→{E} is a partial functional dependency because {C}→{E}