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HTML

<html lang="en">
<head>
    <meta charset="utf-8" />
    <title>jQuery UI Datepicker - Double-Click Issue</title>
    <link rel="stylesheet" href="http://code.jquery.com/ui/1.9.2/themes/base/jquery-ui.css" />
    <script src="http://code.jquery.com/jquery-1.8.3.js"></script>
    <script src="http://code.jquery.com/ui/1.9.2/jquery-ui.js"></script>
</head>
<body>
 
<p>Date1: <input type="text" id="datepicker1" /></p>
<p>Date2: <input type="text" id="datepicker2" /></p>

 
</body>
</html>

JavaScript

Date.prototype.addDays = function(days) {
    var dt = new Date(this.valueOf());
    var ms = dt.getTime() + (86400000 * days);
    var added = new Date(ms);
    return $.datepicker.formatDate('mm/dd/yy', added);
}

$(function() {
    $("#datepicker1").datepicker();
    $("#datepicker2").datepicker();
    $("#datepicker1").change(function() {
        var $d1 = $("#datepicker1");
        var $d2 = $("#datepicker2");
        if ($d2.val() == "" && $d1.val() != "") {
            var d = new Date($d1.val());
            $d2.datepicker("option", "defaultDate", d.addDays(8));
        }
    });
});