Simple way to get element by id within a div tag?

You may try something like this.

Sample Markup.

<div id="div1" >
    <input type="text" id="edit1" />
    <input type="text" id="edit2" />
</div>
<div id="div2" >
    <input type="text" id="edit3" />
    <input type="text" id="edit4" />
</div>

JavaScript

function GetElementInsideContainer(containerID, childID) {
    var elm = {};
    var elms = document.getElementById(containerID).getElementsByTagName("*");
    for (var i = 0; i < elms.length; i++) {
        if (elms[i].id === childID) {
            elm = elms[i];
            break;
        }
    }
    return elm;
}

Demo: http://jsfiddle.net/naveen/H8j2A/

A better method as suggested by nnnnnn

function GetElementInsideContainer(containerID, childID) {
    var elm = document.getElementById(childID);
    var parent = elm ? elm.parentNode : {};
    return (parent.id && parent.id === containerID) ? elm : {};
}

Demo: http://jsfiddle.net/naveen/4JMgF/

Call it like

var e = GetElementInsideContainer("div1", "edit1");