JSFiddle - React, Tailwind, and code Playground

HTML

<div id="textdiv">text</div>
<button id="add">click this</button>

CSS

#textdiv {
    width: 200px;
    height: 200px;
    padding: 20px;
    background-color: #eeeeee;
    overflow-y: auto;
}

JavaScript

var div = $('#textdiv'),
    height = div.height();

$('#add').on('click', function(){
    div.append('<p>Lorem ipsum dolor sit amet, solet nostrud concludaturque no eam. Ne quod recteque pri. Porro nulla zril mei eu. Eu nibh rebum pri, eu est maiorum menandri, ridens tamquam abhorreant te eum. Ipsum definiebas ad mel.</p>');
    div.animate({scrollTop: height}, 500);
    height += div.height();
});