# Partial derivative properties rule

1. Sep 18, 2014

### shabnam

Hi I need help regarding following

can I write following partial derivative wrt x multiplied by Ax

(∂A[x])Ax =∂(Ax^2)

2. Sep 18, 2014

### mathman

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. Sep 18, 2014

### 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,

Last edited: Sep 18, 2014
4. Sep 18, 2014

### Fredrik

Staff Emeritus
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: Sep 21, 2014
5. Sep 21, 2014

### HallsofIvy

Staff Emeritus
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?)