This demo shows the partial derivatives of functions of two variables \(f(x,y)\) at \((x_0,y_0)\). You can think of the partial derivative \(\dfrac{\partial f}{\partial x}(x_0,y_0)\) as the slope of the tangent line of the curve \(f(x,y_0)\) living on the slice plane \(y = y_0\). The slice plane and the slice curve are shown in red in this demo.

You can do the same thing for \(\dfrac{\partial f}{\partial y}(x_0,y_0)\). Think of it as the slope of the tangent line of the curve \(f(x_0,y)\) living on the slice plane \(x = x_0\). The slice plane and the slice curve are shown in blue in this demo.

These two lines span the tangent plane given by \(z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0).\)

You can change settings such as domain and range of the function. For each slider bar, if you click on the plus sign on the right, there will be more settings to play with. For example, you can let a parameter run from \(a\) to \(b\) giving you an animation.

With the current technology, in order to use this demo, you need a CDF Player Plugin for your web browser. You can download it for free from Wolfram. Unfortunately, this cannot be run on any mobile devices. (I really want this, Wolfram.)

By Nics Theerakarn.

This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.