jquery child selector problems

Answer 1

Try this

$('li.parent_folder').click(function() {

  // +this+ var refers to the +li+ that was clicked.

  // .children() gets the children of each element in the set of matched elements, optionally filtered by a selector.
  $(this).children('ul.submenu').hide();
});

Here's more information on jQuery .children() method

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Edit:

updated method from .find() to .children() based on @Gumbo's recommendation

Answer 2

$ does not maintain any kind of magical context - you'll have to tell it if you want to start looking from a certain element. In an even handler, this points to the element the handler is attached to. Try

$(this).find(">ul.submenu").hide();