You can’t do AJAX that way in WP. Basically, none of the functions for WP or any plugins will be defined. See this document on using AJAX in WP https://codex.wordpress.org/AJAX_in_Plugins. You either need to go through admin-ajax.php or you need to load all the WP stuff at the top of your file. The first one is considered the correct way to do this, the second is considered a hack.
