Proof of Formula 4: Derivative of Dot Product of Vector Functions

In this video I derive the 4th differentiation rule for vector functions, which involves taking the derivative of the dot product between two vector functions and yields a similar result as the normal product rule for real-valued functions. I prove this by first expanding the dot product and writing it as a finite sum. Then, by applying summation rules and taking the corresponding product rule for real-valued functions of the summation series, we obtain our proof!

#math #science #calculus #vectors #dotproduct

Timestamps:

- Proof of Formula 4: Expanding the dot product: 0:00
- Writing the dot product as a summation and applying the ordinary product rule: 1:54
- Dot product becomes the product rule of each term in the summation: 4:06
- Splitting into two summation equals Formula 4: 5:24

Notes and playlists:

- Summary: https://inleo.io/threads/view/mes/re-leothreads-36z2oxys7
- Notes: https://peakd.com/hive-128780/@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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