Validating the Chain Rule in Calculus

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  • Thread starter Thread starter Jimmy Chung
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    Chain Chain rule Proof
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Discussion Overview

The discussion revolves around the validity of a proof for the chain rule in calculus. Participants are examining the reasoning and assumptions behind the proof, questioning its correctness and potential circular reasoning, particularly regarding the treatment of the error term as it approaches zero.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions the validity of the proof, suggesting there may be circular reasoning involved with the error term approaching zero.
  • Another participant expresses skepticism about the trustworthiness of the textbook from which the proof is derived, asking for specific points of concern.
  • A participant seeks clarification on a specific part of the proof regarding the transition from E(g2) to E(g(x)), questioning why the limit of E(g(x)) as h approaches 0 is considered to be 0.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the validity of the proof. Multiple competing views and concerns about the reasoning presented remain unresolved.

Contextual Notes

There are indications of missing assumptions regarding the error term and its behavior as h approaches 0, as well as potential dependencies on definitions that are not fully explored in the discussion.

Jimmy Chung
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Is this proof of the chain rule valid ?
 

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How did you get this?
Did you write this yourself?
 
It's from a textbook...I just re-typed it into a word doc...
 
Is it correct...I suspect there maybe some circular reasoning with the "error term" becoming 0 as h approaches 0.
 
It looks valid to me, but just tell us why you do not trust your book. At which part.
 
Can you explain to be the part on the bottom when we set g2=g(x+h) but E(g2) turns into E(g(x)) not E(g(x+h)) ?

If that's valid, why is the limit as h approaches 0 of E(g(x)) is 0 ?
 

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