On implementing a destructor of the derived class, is there any need for the explicit calling of the destructor for my base class?

 No, there is no need to call the destructor explicitly except in the case of placement hew. A destructor of a class, whether you explicitly define one or not, invokes a destructor automatically for base class sub objects. Base classes are destructed after member objects. In the multiple inheritance, the destruction of the direct base classes occur in the reverse order of their appearance in the inheritance list.
Example: