Recall from Lab 2 that the partial derivatives of a function f(x,y) at
a point (x0,y0) can be found by looking the x- and y-slice curves of
the function graph and then calculating the slopes of the tangent lines
to these curves at (x0,y0,f(x0,y0). For the directional derivative,
instead of slicing along the positive x- and y-directions, we slice the
graph along a direction (cos θ, sin θ). The slope of the tangent line
to the slice curve at (x0,y0, f(x0,y0) is the directional derivative.
The demo allows you to choose a point (x0,y0) in the domain as well as
a direction (cos θ, sin θ) using the two orange hotspots. The graph is
shown in a separate window with the corresponding slice curve and
slicing plane. The third window shows the slice curve in its plane
along with the tangent line.