596C.C4.1 Rethinking the Meaning of Derivative: Real Case

Geogebra tool for derivative of real functions: https://www.geogebra.org/classic/my2f... 0:00 Introduction 1:15 A Grad School Story 2:38 Sophistication 1: Real Tangent Vectors 5:44 LOCATIONS are not DIRECTIONS 7:07 Limit Definition of Derivative 8:05 Slope of a Tangent Line 8:43 Reframing "Slope" as "Ratio" 9:38 Slope is a Relationship of Tangent Vectors 10:55 Visualizing the Derivative as Ratio of Tangent Vectors 14:33 Derivative is a Linear Transformation