YouTube - Summary - Notes - Playlist - Vector Functions playlist
In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of a vector function is defined as the limit as h approaches zero of the secant vector (difference of two vectors separated by incrementing the parameter t by h) divided h. As h approaches zero the secant vector approaches a vector that is parallel to the tangent vector to the curve.
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Timestamps
Introduction to Derivatives and Integrals of Vector Functions: 0:00
Definition of Derivative of a Vector Function: 0:15
Secant vector is the vector between the position vectors in the definition of derivative: 1:36
Tangent vector is secant vector multiplied by 1/h as h approaches zero: 4:28
GeoGebra animation of the secant line approaching the tangent line: https://www.geogebra.org/m/sVCRDDmA 7:17
Unit Tangent Vector is the tangent vector divided by its magnitude: 10:16
