What Is the Order of Derivatives in Variable v?

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Discussion Overview

The discussion revolves around the concept of the "order" of a variable v and its derivatives, specifically ∂v/∂x and ∂2v/∂x2. Participants explore the implications of v being of order δ, including the interpretation of "order" in the context of derivatives and potential confusion surrounding the terminology.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants inquire about the meaning of "order" in relation to derivatives, noting that first-order derivatives are typically represented as dy/dx or ∂y/∂x, while second-order derivatives are represented as d²y/dx² or ∂²y/∂x².
  • One participant suggests that the differentiation power rule should be considered when determining the order of the derivatives.
  • Another participant questions the meaning of stating that a function is "of order δ," indicating a lack of clarity on the term.
  • Some participants propose that if v is a derivative, then δ could represent an nth order derivative, which would affect the order of the other derivatives mentioned.
  • There is a suggestion that the question may be a trick question, reflecting uncertainty about the intent behind the original query.
  • Several participants express a need for additional context from the original poster to clarify the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the meaning of "order" in this context, and multiple competing interpretations remain. The discussion reflects uncertainty and differing viewpoints regarding the terminology and implications of the order of derivatives.

Contextual Notes

Limitations include a lack of clarity on the definition of "order" as used by the original poster and the absence of specific context for the question posed.

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If v is of order δ, what is the order of ∂v/∂x and ∂2v/∂x2 ?
 
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vktsn0303 said:
If v is of order δ, what is the order of ∂v/∂x and ∂2v/∂x2 ?

I have never seen those symbols used before but I think I understand the problem

I believe that in this case you would have to take the differentiation power rule into account
 
vktsn0303 said:
If v is of order δ, what is the order of ∂v/∂x and ∂2v/∂x2 ?
What do you mean by "order"? Order is usually used in reference to derivatives, with dy/dx and ∂y/∂x being first-order derivatives, and with ##\frac{d^2y}{dx^2}## and ##\frac{\partial^2y}{\partial x^2}## being second-order derivatives.

##x^2 + 3x## is a polynomial of degree two, while ##t^4 - 3t^2 + 7## is a polynomial of degree four. So what do you mean by "v is of order δ"?
 
What does it mean to say that a function is "of order \delta?
 
What if v is a derivative? So if δ were n, v would be an nth order derivative, making the other two...

Sorry, only thing that makes any sense to me. Seems to be some sort of trick question.
 
Battlemage! said:
What if v is a derivative? So if δ were n, v would be an nth order derivative, making the other two...

Sorry, only thing that makes any sense to me. Seems to be some sort of trick question.
Some context here from the OP would be helpful, although it's been a week since the question was posted, so we might never know.
 
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