JSFiddle - React, Tailwind, and code Playground
HTML
<button onclick="AddLine();">Add some text</button>
<div id="outer">
<div id="inner">
</div>
</div>
CSS
#outer
{
height:120px;
border:solid 1px black;
overflow-y:auto;
}
JavaScript
var lineCount = 1;
function AddLine()
{
$('#inner').append(lineCount + ' Adding a line of text<br/>');
lineCount++;
var outerTop = $('#outer').scrollTop();
var outerBottom = outerTop + $('#outer').height();
var innerTop = $('#inner')[0].offsetTop;
var innerBottom = innerTop + $('#inner').height();
if (innerBottom > outerBottom)
$('#outer').scrollTop(innerBottom - $('#outer').height());
}