In the demo, the gray surface is the graph of f(x,y). If you check one of the partial derivative checkboxes ("f_x" or "f_y") you will be shown a graph of that partial derivative in the "First Partial Derivatives" window as well as a series of curves in the "Function Graph" window. The white curves are slices of the function graph, and the red or green curves show the values of the partial derivative for those slices of the surface. This shows how partial derivatives for functions of two variables relate to derivatives in one-variable calculus.

There are also four checkboxes for second partial derivatives. You can use these to view the surface for any of the second partial derivative functions as well as slice curves of the first partial derivative graph and curves showing the second partial derivative at those slices. This demonstrates that once you know how to find partial derivatives, you can easily find the second partial derivative by taking the partial derivative of a function which is itself a partial derivative of another function.

The second partial derivative graphs are colored as follows:

Yellow = fxx(x,y)
Magenta = fyx(x,y)
Blue = fxy(x,y)
Cyan = fyy(x,y)