Partial derivative properties rule

  • Thread starter shabnam
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  • #1
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Hi I need help regarding following

can I write following partial derivative wrt x multiplied by Ax

(∂A[x])Ax =∂(Ax^2)
 

Answers and Replies

  • #2
mathman
Science Advisor
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Hi I need help regarding following

can I write following partial derivative wrt x multiplied by Ax

(∂A[x])Ax =∂(Ax^2)

Usually they would by interpreted differently. The left side is Ax multiplied by the derivative of Ax, while the right side is the derivative of the square.
 
  • #3
What do you mean by the square brackets on the LHS? I.e., does it mean A is a function of x or is it an unnecessary bracket?


Are you asking does the following hold true
[tex]
\left( \frac{\partial}{\partial x} \left( Ax \right) \right) Ax = \frac{\partial}{\partial x} \left( (Ax)^{2} \right)
[/tex]


(i.e., is the derivative of the square of the function##Ax## wrt x (right hand side) equal the derivative of the function ##Ax## multiplied by ##Ax##)

?

Or is A a constant? If so then they aren't the same thing,
 
Last edited:
  • #4
Fredrik
Staff Emeritus
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Gold Member
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Hi I need help regarding following

can I write following partial derivative wrt x multiplied by Ax

(∂A[x])Ax =∂(Ax^2)
It's impossible to know what you mean by that notation. You have to provide more information when you ask a question.

Looks like more than one person in this thread might find the LaTeX FAQ useful. https://www.physicsforums.com/showthread.php?p=3977517#post3977517
 
Last edited:
  • #5
HallsofIvy
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Do you mean
[tex]\frac{\partial Ax}{\partial x} Ax= \frac{\partial Ax^2}{\partial x}[/tex]?

Is A a constant? If so it is clear that those are not the same:
[tex]\frac{\partial Ax}{\partial x}Ax= A^2x \frac{\partial x}{\partial x}= A^2x[/tex]
while
[tex]\frac{\partial Ax^2}{\partial x}= A\frac{\partial x^2}{\partial x}= 2Ax[/tex]

(Why did you want to treat this as a partial derivative when there is only the one variable, x?)
 

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