echo "<table class='table'>".
        "<thead>".
             "<tr>".
                "<td>ID</td>".
                "<td>url_video</td>".
             "</tr>".
        "</thead><tbody>";
while($valor = mysqli_fetch_array($resultado)){
    echo "<tr>".
            "<td>".$valor['ID']."</td>".
            "<td><input type='text' value='".$valor['url_video']."'  style='width: 400px;' id='url-video'></td>".
            "<td><input type='button' value='Update' class='btn-update' data-id='".$valor['ID']."' >"."</td>".
         "</tr>";
}
echo "</tbody></table>";

$(document).ready(function(){

    $('.btn-update').click(function(){
        var id = $('.btn-update').data('id');
        var string = $('.url_video').val();

        $.ajax({
            url: "tabelaUpdate.php",
            data: { 'idDeUpdate' : id,
                    'url_video' : string
                  },
            type: "POST",
            cache: false,
            success: function(response){
                //alert("ok"+response);
                $('#result').html(response); //serve para ver a array foi inserida mesmo
            }
        })
    });
});