# Partial derivative properties rule

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.

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:
Fredrik
Staff Emeritus
Gold Member
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:
HallsofIvy
$$\frac{\partial Ax}{\partial x} Ax= \frac{\partial Ax^2}{\partial x}$$?
$$\frac{\partial Ax}{\partial x}Ax= A^2x \frac{\partial x}{\partial x}= A^2x$$
$$\frac{\partial Ax^2}{\partial x}= A\frac{\partial x^2}{\partial x}= 2Ax$$