How can I automatically render a preview when the scene has changed? I have a split screen with my render on the right on very low sample rate so the render will happen quite quickly.  On the left, I have my 3d camera perspective for my modeling and object manipulation.  What I would like is to have the right side update the render when my objects on the left are changed automatically.  Is there a setting for this?  I already have the Update Automatically checked under the view menu however it doesn't seem to affect anything.  Thanks for your help.
Just do the preview render in the viewport itself and set the viewport shading to "Rendered". Also type Numpad-0 to set the view and check "Border" to render only the important parts.

Everything you edit on the left side will cause the right screen to re-render.