Partial derivative problem

geekba

Hi!
Here is my function:



My task is to find:



I think I know how to find ∂u/∂x, but I have no idea how to find ∂/∂z(∂u/∂x). Here is how I found ∂u/∂x:

http://oi48.tinypic.com/prsly.jpg

Does someone know how to find ∂/∂z(∂u/∂x)?
I appreciate any help :)

Sourabh N

Before the second partial derivative, you should fix the error in your calculation of ∂u/∂x, specifically ∂([itex]\frac{xy}{z}[/itex])/∂x.

geekba

What's wrong with ∂(xy/z)/∂x? I checked it and it seems correct to me...

geekba

It's very important so all suggestions are welcome :)

Sourabh N

Never mind. I hadn't scrolled all the way down, it is correct.

I believe you are having trouble calculating [itex]\frac{∂}{∂z}[/itex]([itex]∂\rho/∂s[/itex]) and [itex]\frac{∂}{∂z}[/itex]([itex]∂\rho/∂t[/itex]) (Let me know if this is not the case).
To simplify this, get rid of s and t by writing [itex]∂\rho/∂s[/itex] and [itex]∂\rho/∂t[/itex] as partial derivatives of [itex]\rho[/itex] w.r.t. x, y and z, using the chain rule. Since you know how s and t depend on x, y and z, this can be done.

Once you have done this, calculating [itex]\frac{∂}{∂z}[/itex]([itex]∂\rho/∂s[/itex]) and [itex]\frac{∂}{∂z}[/itex]([itex]∂\rho/∂t[/itex]) would be straightforward.

geekba

I got it finally Thaks a lot!