ex.js

$('#first-element').daterangepicker(
  { 
     // options 
  }, 
  function(start, end, label) {
    
    $('#first-hidden-input').val(start.format('YYYY-MM-DD'));
    
    var 7_days_ahead = moment(start).add(7, 'days');
    $('#second-element').data('daterangepicker').setStartDate(7_days_ahead);
    
  }
);

$('#second-element').daterangepicker(
  { 
    //options
  },
  function(start, end, label) {
    
    $('#second-hidden-input').val(start.format('YYYY-MM-DD'));
    
  }
);