Detect change to selected date with bootstrap-datepicker

I have an input element with an attached datepicker created using bootstrap-datepicker.

<div class="well">
    <div class="input-append date" id="dp3" data-date="2012-01-02" data-date-format="yyyy-mm-dd">
        <input type="text" id="date-daily">
        <span class="add-on"><i class="icon-th"></i></span>    
    </div>
</div>

<script language="JavaScript" type="text/javascript">
    $(document).ready(function() {
        $('#dp3').datepicker();
        $('#date-daily').val('0000-00-00');
        $('#date-daily').change(function () {
            console.log($('#date-daily').val());
        });
    });
</script>

When the user changes the date by typing directly into the input element, I can get the value with the input element's onChange event, as shown above. But when the user changes the date from datepicker (i.e. by clicking a date on the calendar), the onChange handler is not called.

How can I detect changes to the selected date that are made via the datepicker, rather than by typing into the input element?