The thing is that your ajax response is returning a string, so if you use directly $(response) it would return JQUERY: Uncaught Error: Syntax error, unrecognized expression in the console. In order to use it properly you need to use first a JQUERY built-in function called $.parseHTML(response). As what the function name implies you need to parse the string first as an html object. Just like this in your case:
$.ajax({
url: url,
cache: false,
success: function(response) {
var parsedResponse = $.parseHTML(response);
var result = $(parsedResponse).find("#result");
alert(response); // returns as string in console
alert(parsedResponse); // returns as object HTML in console
alert(result); // returns as object that has an id named result
}
});