YouTube - Summary - Notes - Playlist - Vector Functions playlist
In this video I go over the six main differentiation rules for vector functions, as well as the 2nd (or higher) derivatives. The rules have their similar counterparts for real valued functions, and I leave the proofs for later videos. Deriving each rule involves either applying the definition of a derivative for a vector function or applying the theorem of differentiating functions by components.
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Timestamps
Second derivative of a vector function is just the derivative of the derivative: 0:00
Differentiation rules have counterparts for real-valued functions: 1:48
Formula 1: Derivative of Addition of Vector functions: 2:20
Formula 2: Constant multiple: 3:00
Formula 3: Real-valued function multiple: 3:27
Formula 4: Dot product: 4:15
Formula 5: Cross product: 5:08
Formula 6: Chain rule: 5:50
Screenshot of the 6 differentiation rules from my Calculus Book: 6:50
