Where Does This Equation Originate?

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Discussion Overview

The discussion revolves around the origin and validity of a specific mathematical equation involving derivatives and logarithms. Participants explore the relationship between different forms of the equation and seek to understand whether they can be proven equivalent. The scope includes mathematical reasoning and clarification of derivative rules.

Discussion Character

  • Mathematical reasoning, Technical explanation

Main Points Raised

  • One participant presents an equation involving derivatives and logarithms and questions its origin.
  • Another participant suggests that the equation may be derived from the chain rule, indicating a potential equivalence.
  • A third participant confirms the correctness of the relation proposed by the second participant and inquires about the possibility of expressing the original equation in a similar form.
  • A fourth participant seeks validation of their own relation involving integrals and logarithms, questioning its correctness in relation to the earlier discussions.

Areas of Agreement / Disagreement

Participants express varying interpretations of the equations and their relationships. There is no consensus on the correctness of the original equation or the proposed relations, leading to an unresolved discussion.

Contextual Notes

Participants do not clarify certain assumptions or dependencies in their equations, and the discussion lacks resolution on the mathematical steps involved in proving the relationships.

pattisahusiwa
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I have an equation like this,

[itex]\frac{dZ}{zD\beta} = \frac{d}{d\beta}\ln Z[/itex],

is it from [itex]\frac{d}{d\beta}\frac{dZ}{Z}[/itex] or from...?

How we can prove this relation?
 
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Is your equation supposed to be
[tex]\frac{1}{Z} \frac{ dZ}{d\beta} = \frac{d}{d\beta} \ln(Z)[/tex]
If so, this is just the chain rule
 
Thank you for quick replay.

Yes, your relation is correct too. If this is a chain rule, so can i write them like one in the first thread?
 
Hi all, I just want to know that my relation is correct or not?

[tex]\frac{1}{Z}\frac{dZ}{d\beta} = \frac{d}{d\beta}\int\frac{dZ}{Z} = \frac{d}{d\beta}\left(\ln Z\right)[/tex]
 

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