Geometric examination of the directional derivative of a function of two variable.

Drag the point A in the left pane to choose the point at which to examine the directional derivative. The vector u controls the direction along the surface; We consider the blue curve of intersection of the surface with the vertical plane containing the vector u. The slope of the tangent line to this curve (within the vertical plane) at the point C IS the directional derivative of the function at A in the direction of u.
To approximate this tangent line slope, we look at the limit of secant line slopes through points C and E on the curve (controlled by the slider variable h) as h approaches 0. To get a good estimate of the tangent line slope of the curve at C, average the slopes for the smallest positive and smallest negative values of h (0.05 and -0.05, rexpectivly).