JSFiddle - React, Tailwind, and code Playground

HTML

<input type="text" id="date1" value="01/01/15">
<input type="text" id="date2" value="01/01/15">

JavaScript

$(function () {
    $('#date1').change(function () {
        var value = $(this).val(),
            split = value.split('/'),
            day = split[0],
            month = parseInt(split[1]) - 1 // months start counting from 0
            ,
            year = split[2];
        year = lpad(year);
        var date = new Date(Date.UTC(year, month, day));

        // add one day 
        date.setDate(date.getDate() + 1);

        // format final 
        var final = lpad(date.getDate()) + '/' + lpad((date.getMonth() + 1)) + '/' + date.getYear()
        $('#date2').val(final);
    });
});

// add leading zero
function lpad(n) {
    n = (n <= 9) ? "0" + n : n;
    return n;
}