Finding Partial Derivatives of a Multivariable Function

geekba
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Hi!
Here is my function:

2ag2fia.jpg


My task is to find:

206irmv.jpg


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 :)
 
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Before the second partial derivative, you should fix the error in your calculation of ∂u/∂x, specifically ∂(\frac{xy}{z})/∂x.
 
What's wrong with ∂(xy/z)/∂x? I checked it and it seems correct to me...
 
It's very important so all suggestions are welcome :)
 
geekba said:
What's wrong with ∂(xy/z)/∂x? I checked it and it seems correct to me...

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

I believe you are having trouble calculating \frac{∂}{∂z}(∂\rho/∂s) and \frac{∂}{∂z}(∂\rho/∂t) (Let me know if this is not the case).
To simplify this, get rid of s and t by writing ∂\rho/∂s and ∂\rho/∂t as partial derivatives of \rho 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 \frac{∂}{∂z}(∂\rho/∂s) and \frac{∂}{∂z}(∂\rho/∂t) would be straightforward.
 
I got it finally :smile: Thaks a lot!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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