Order δ: ∂v/∂x & ∂2v/∂x2

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In summary, the conversation seems to revolve around the differentiation power rule and the concept of function order in relation to derivatives.
  • #1
vktsn0303
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If v is of order δ, what is the order of ∂v/∂x and ∂2v/∂x2 ?
 
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  • #2
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
 
  • #3
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"?
 
  • #4
What does it mean to say that a function is "of order [itex]\delta[/itex]?
 
  • #5
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.
 
  • #6
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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What is the definition of order δ: ∂v/∂x & ∂2v/∂x2?

The order δ: ∂v/∂x & ∂2v/∂x2 refers to the order of a differential equation, which is determined by the highest derivative present in the equation. In this case, δ represents a variable order, meaning that it can take on different values depending on the specific equation being analyzed.

How is order δ: ∂v/∂x & ∂2v/∂x2 calculated?

The order δ: ∂v/∂x & ∂2v/∂x2 is calculated by looking at the highest derivative present in the equation. For example, if the equation is ∂3v/∂x3 + 2∂v/∂x = 0, the order would be δ = 3.

What is the significance of order δ: ∂v/∂x & ∂2v/∂x2 in differential equations?

The order δ: ∂v/∂x & ∂2v/∂x2 helps determine the complexity and behavior of a differential equation. It can also provide information about the number of initial conditions needed to solve the equation and the existence of a unique solution.

What is the difference between ∂v/∂x and ∂2v/∂x2?

∂v/∂x is the first derivative of v with respect to x, while ∂2v/∂x2 is the second derivative of v with respect to x. In other words, ∂2v/∂x2 is the rate of change of the rate of change of v with respect to x.

How does order δ: ∂v/∂x & ∂2v/∂x2 affect the solution of a differential equation?

The order δ: ∂v/∂x & ∂2v/∂x2 can affect the complexity and type of solution for a differential equation. Higher orders can lead to more complex solutions, while lower orders may have simpler solutions. Additionally, different orders may require different initial conditions for a unique solution to exist.

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