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.