Derivative for Vector Functions by Components + Proof

In this video I show that the derivative of a vector function is equal to the derivative of the real-valued functions in its components. I prove this by applying the definition of derivatives for vector functions, and then apply basic limit and vector laws to obtain the corresponding definition of derivative of each real-valued function in each component. This is a straight forward proof, and the result means that to obtain the derivative of a vector function, we just take the derivative of it components!

#math #science #calculus #vectorfunctions #proof

Timestamps:

- Theorem: Derivative of Vector Functions by Components: 0:00
- Proof: Using Definition of Derivative of Vector Functions: 1:26
- Definition of Derivative of real-valued functions in each component of the vector function: 6:04
- Derivative is just the derivative of components of the vector function: 7:08

Notes and playlists:

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