# Homework Help: Partial Differentiation Confusion

1. Jan 5, 2010

### RazerM

1. The problem statement, all variables and given/known data
Find $$\frac{\partial z}{\partial x} \frac{\partial z}{\partial y}$$ where $$z=\left( [x+y]^3-4y^2 \right)^{\frac{1}{2}}$$

2. Relevant equations
-

3. The attempt at a solution
I know that $$\frac{\partial z}{\partial y}=\frac{3(x+y)^2-8y}{2\sqrt{(x+y)^3-4y^2}}$$
but I am unsure whether $$\frac{\partial z}{\partial x}$$ is the exact same or does not include the '-8y' in the numerator.

I get the feeling that when finding the derivative inside the square root (in z) that y should still be treated as constant and therefore have no -8y.

Last edited: Jan 5, 2010
2. Jan 5, 2010

### tiny-tim

Welcome to PF!

Hi RazerM! Welcome to PF!

(on this forum, you need to type "tex", not "TEX" )
Yes, that's completely correct.

∂z/∂x means "keeping y constant", so that's exactly what you do!

3. Jan 5, 2010

### RazerM

Re: Welcome to PF!

So that means $$\frac{\partial z}{\partial x}=\frac{3(x+y)^2}{2\sqrt{(x+y)^3-4y^2}}$$?

4. Jan 5, 2010

### tiny-tim

Yup!

(nice LaTeX, btw )

5. Jan 5, 2010

### RazerM

Thanks :)

I taught myself to use LaTeX to help me with my Physics Investigation as part of Advanced Higher Physics (Highest level of physics taught in school - Scotland), we never got told to use it but no way was I using MS Office or Openoffice's limited equation typesetting, would have been a nightmare :P

6. Jan 5, 2010

### tiny-tim

One of the many benefits of PF membership is that you can now use LaTeX as much as you like!

(in case you haven't found anything similar, a useful bookmark is http://www.physics.udel.edu/~dubois/lshort2e/node61.html#SECTION008100000000000000000" [Broken] )

Last edited by a moderator: May 4, 2017