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: @mes/re-leothreads-wjvwxmxy
• Notes: @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: @mes

Email me: contact@mes.fm

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