The best free alternative to DHTMLX is jQuery, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 10 alternatives to DHTMLX and 17 is free so hopefully you can find a suitable replacement. Other interesting free alternatives to DHTMLX are Zepto.js (Free, Open Source), Umbrella JS (Free, Open Source), Dojo Toolkit (Free, Open Source) and Prototype JS (Free, Open Source).
Intuitive and Documented It is strongly influenced by jquery with many similar methods so you'll feel at ease developing with Umbrella. However there are also some improvements such as with .ajax(), .append(), etc.