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 .
Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
Email me: [email protected]
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
▶️ 3Speak