Ln(x^2+y^2) with directional derivative

You can see how the directional derivative will change as you move the vector in the xy-plane that indicates the direction you will move along the surface. To move the vector, click the selection tool (arrow), and drag the arrow end of the vector around. To get a good view of what is happening on the surface, note that the first point of the vector (2,1,0) is connected to the corresponding point on the surface, and as you move the other end of the vector, the vertical plane that contains the vector also moves. You can then click the "rotate" icon to be able to grab and rotate the axes for a good view of how the height on the surface is changing relative to movement along that particular vector in the xy-plane.