Differentiation Rules for Vector Functions

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

• Summary: @mes/re-leothreads-2pbvvk4am
• Notes: @mes/hfsetrue
• Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FgQ3jBd9IFaWOakOWbHous
• Vector Functions playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FgQ3jBd9IFaWOakOWbHous .

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