JSFiddle - React, Tailwind, and code Playground

HTML

<script src="http://ajax.aspnetcdn.com/ajax/jquery.validate/1.11.1/jquery.validate.min.js"></script>
<script src="http://ajax.aspnetcdn.com/ajax/jquery.validate/1.11.1/additional-methods.js"></script>
<form id="myform">
    <input name="product[0][name]" id="form_product[0][name]" data-rule-required="true" />
    <input name="product[1][name]" id="form_product[1][name]" data-rule-required="true" />
    <input name="product[2][name]" id="form_product[2][name]" data-rule-required="true" />
    <br/>
    <br/>
    <br/>
    <input type="submit" />
</form>
<br/>
<br/>
<button>add one field</button>
<a id="docs" href="http://docs.jquery.com/Plugins/Validation" target="_blank">Validation Documentation</a>

CSS

#docs {
    display: block;
    position: fixed;
    bottom: 0;
    right: 0;
}

JavaScript

$(document).ready(function () {

    $('#myform').validate({ // initialize the plugin      
        submitHandler: function (form) { // for demo
            alert('valid form submitted'); // for demo
            return false; // for demo
        }
    });

    $('button').one('click', function () {
        $('#myform').append('<input name="product[3][name]" id="form_product[3][name]" data-rule-required="true">');
    });

});