Deriving a Non-Formula Field Using an After Field Changed Trigger

If you want the end-user to see the derived field's value update on the user interface immediately, then you need to perform the assignment of the derived field's value inside an After Field Changed trigger.

When this trigger fires, the value of the field in question has already changed. Therefore, you can simply reference the new value of the field by name instead of using the special newValue expression (as would be required in a field-level validation rule to reference the field's candidate new value that is attempting to be set).