I know its too late to answer, but in my scenario below code was not working.
$('#datepicker').val("");
$('#datepicker').val('').datepicker('update');
$('#datepicker').datepicker('update','');
here is my solution.
$('#datepicker').val('').datepicker('remove').datepicker();
I did clear datepicker value first then removed datepicker and again reinitialize datepicker. its resolved my problem.