Derivative of Arctan(x)

If we measure the derivative of arctan(x) and record the values, we trace out the derivative. Compare the derivative of arctan(x) with 1/(1 + x^2). How can we show these two are the same thing?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Jason McCullough, Created with GeoGebra