Exercise 5: Proof of Formula 6: Chain Rule for Vector Functions

In this video I prove Formula 6 of the differentiation rules for vector functions and this time show that the derivative of a vector function whose parameter is a real valued function results in a counterpart of the chain rule. In other words, the derivative of the vector functions in terms of the parameter t becomes the derivative of the real-valued function in terms of the parameter t multiplied by the derivative vector function in terms of the parameter f(t).

#math #vectors #calculus #chainrule #education

Timestamps:

- Exercise 5: Proof of Formula 6: Derivative of a Function within a Vector Function: 0:00
- Solution: Taking derivative of components: 1:05
- Applying chain rule for each component: 2:54
- Factor out the real-valued function: 3:46
- We obtain our chain rule for vector functions: 4:21

Notes and playlists:

- Summary: https://inleo.io/threads/view/mes/re-leothreads-2yynuofgg
- 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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