Question on form of differential

[Noone1982]

My book says:

let p stand for partial, u is a function

p(uAx) / px = pu(Ax)/px + up(Ax)/px

How can it be valid?

 

[amcavoy]

My book says:

let p stand for partial, u is a function

p(uAx) / px = pu(Ax)/px + up(Ax)/px

How can it be valid?

First of all, what is u a function of? Second, did you mean A(x)?

 

[Noone1982]

u is just say xyz and Ax means A subscript x

 

[Integral]

It would help us all if you would take a few minutes to read through this thread . LaTex is really very easy and it makes it much easier to present problems such as yours.

 

[Noone1982]

$$\frac{\partial }{\partial x}\left( uA_{x} \right)\; =\; \frac{\partial u}{\partial x}\left( A_{x} \right)+u\frac{\partial A_{x}}{\partial x}$$

To me, the right hand of the equation is saying the left hand twice rather than reworking it.

 

[Manchot]

That's just the straight-up definition of the chain rule.

 

[Noone1982]

Thanks! :)