Partial derivative properties rule

[shabnam]

Hi I need help regarding following

can I write following partial derivative wrt x multiplied by Ax

(∂A[x])Ax =∂(Ax^2)

 

[mathman]

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.

 

[DabblingMathmo]

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
$$\left( \frac{\partial}{\partial x} \left( Ax \right) \right) Ax = \frac{\partial}{\partial x} \left( (Ax)^{2} \right)$$


(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,

 

[Fredrik]

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

 

[HallsofIvy]

Do you mean
$$\frac{\partial Ax}{\partial x} Ax= \frac{\partial Ax^2}{\partial x}$$?

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

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