Undergrad What Is the Order of Derivatives in Variable v?

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If v is of order δ, then the order of its first derivative ∂v/∂x is δ - 1, and the order of its second derivative ∂2v/∂x2 is δ - 2, following the differentiation power rule. The term "order" typically refers to the degree of derivatives, with first-order and second-order derivatives clearly defined. There is some confusion regarding the meaning of "v is of order δ," as it may imply that v itself could be a derivative. The discussion highlights the need for clarity in the original question, as the context is essential for accurate interpretation. Overall, understanding the order of derivatives is crucial in calculus and differential equations.
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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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