Try:
$('#mydiv').find('.myclass');
JS Fiddle demo.
Or:
$('.myclass','#mydiv');
JS Fiddle demo.
Or:
$('#mydiv .myclass');
JS Fiddle demo.
References:
find().- Selector context.
Good to learn from the find() documentation:
The .find() and .children() methods are similar, except that the
latter only travels a single level down the DOM tree.