Exploring Partial Derivatives in GeoGebra 3D

Link to typed up directions: https://bit.ly/2S2nesk

In this video we use GeoGebra 3D (head to geogebra.org and pick the 3D graphing calculator) to get a sense of what partial derivatives really are and how we can visualize them. We're trying to answer the question, "But what are they?" We focus on partial x, dz/dx, but repeat the construction for partial y at the end.

Specifically we: plot a curve, plot a vertical plane, plot the trace of the curve in the plane, put a point on the trace, calculate the appropriate partial derivative, and write the equation of the line tangent to the trace at the point in the plane. There's a lot going on and we use some sliders to make things more dynamic.

Being able to see what you're talking and thinking about helps a ton. Even just playing around with this kind of construction once or twice can help you picture it in your head going forward.

Видео Exploring Partial Derivatives in GeoGebra 3D канала turksvids