I would add a common class name to all required fields. Then on change, for each field with this class name, see if any are empty. If not, hide submit, else show submit.

For this type of thing, where the field type is unknown, you can do a check for field type. Here is an example of a function I use called Attach instead of the change method. Unlike change, it will execute my function on fields of type input or select without specifying.

 

//Simple method for replacing the common, on change
//Usage Attach(function, 'className1', 'className2', 'etc');
function Attach() {
    var func = arguments[0];
    for (var i = 1; i < arguments.length; i++) {
        if ($('.' + arguments[i]).has('input').length > 0) {
            $('.' + arguments[i] + ' input').on('change', func);
        } else if ($('.' + arguments[i]).has('select').length > 0) {
            $('.' + arguments[i] + ' select').on('change', func);
        }
    }
}