以上内容可以通过以下代码实现-

The above can be achieved by following code -

 $('input[name="arrivalDate"]').datepicker({

     //your other configurations.     

     onSelect: function(){
     var start = $('input[name="arrivalDate"]').val();
     var nights = $('input[name="numOfNights"]').val();
     var date = new Date(start);
     var d = date.getDate();
     var m = date.getMonth();
     var y = date.getFullYear();
     var edate= new Date(y, m, d+nights);
     $('input[name="departureDate"]').val(edate);
    }
 });