Update cart with WooCommerce ajax

You have forget this essential process:

add_action('wp_enqueue_scripts', 'add_my_ajax_scripts'); 

function add_my_ajax_scripts() {
    // Here you register your script located in a subfolder `js` of your active theme
    wp_enqueue_script( 'ajax-script', get_template_directory_uri().'/js/script.js', array('jquery'), '1.0', true );
    // Here you are going to make the bridge between php and js
    wp_localize_script( 'ajax-script', 'cart_ajax', array( 'ajaxurl' => admin_url( 'admin-ajax.php' ) ) );
}

Then you will retrieve "ajaxurl" and "cart_ajax" in your javascript file in "url:":

$.ajax({
  url: cart_ajax.ajaxurl,
  ...
})

Your javascript function will not work. Here are some functional examples of what you need to do:

• WooCommerce - auto update total price when quantity changed?

• Wordpress passing ajax value to a specific page using Wordpress

• Using AJAX With PHP on Your WordPress Site Without a Plugin

• How to use Ajax with your WordPress Plugin or Theme?