Differentiation Rules for Vector Functions

about 8 hours ago

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.

#math #science #calculus #vectors #education

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

Notes and playlists: