Exercise 1: Taylor Derivatives Equal the Function's Derivatives at x = a

▶️ Watch on 3Speak

---

In this video I prove that the derivatives of a Taylor Polynomial are equal to the derivatives of the corresponding function used in the approximation when x = a. This is because any derivative at x = a of any Taylor polynomial cancels out all the terms (since a - a = 0) except the first term, which is just the corresponding derivative of f at x = a.

Timestamps:

• Exercise 1: Taylor Derivatives are the same as the function used in the Taylor Polynomial: 0:00
• Solution: Taylor derivatives cancel out all the terms except the first: 0:30
• n-th Taylor derivative is equal to the n-th derivative of f: 8:09

Full video, notes, and playlists:

• Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0F76sIU8xm09oqBTq1mlry3
• HIVE notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials
• Infinite Sequences and Series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

---

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