Actually here the problem is 'Master Page with JQuery', Control Id's are Changed when the page is rendered(if you used Master Page). I think you need use
Control.ClientID
Property.
Try this. it will works.
<script type="text/javascript">
$(function() {
$("#<%=txt_AppointDate.ClientID%>").datepicker({ dateFormat: 'dd/mm/yy', showSpeed: 'fast' });
});
</script>