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## Homework Statement

Given that z = √3x/y show that:

## Homework Equations

∂

^{2}z/∂x∂y = ∂

^{2}z/∂y∂x

## The Attempt at a Solution

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- Thread starter Needhelp2013
- Start date

- #1

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Given that z = √3x/y show that:

∂

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- #2

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Both sides of that equation are the same, did you mistype something?

- #3

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Yes I did, thats it sorted now.

- #4

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Ahh, as I suspected. Have you made an attempt yet?

- #5

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- #6

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I think you're thinking too hard, you know how to take a partial derivative I assume?

- #7

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The equation under "Relevant Equations" is what you're trying to show, correct?

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- #9

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I tried substituting what 'z=' into the laplace equation but that didnt get me anywhere.

Exactly what I meant by thinking too hard. All that it's asking you to do is show that if you take the derivative of z with respect to x and then y, it's the same as taking the derivative of z with respect to y and then x. In other words, show:

[itex]\frac{\partial}{\partial y}(\frac{\partial z}{\partial x}) = \frac{\partial}{\partial x}(\frac{\partial z}{\partial y}) [/itex]

Does that make any more sense now?

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- #11

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Exactly what I meant by thinking too hard. All that it's asking you to do is show that if you take the derivative of z with respect to x and then y, it's the same as taking the derivative of z with respect to y and then x. In other words, show:

[itex]\frac{\partial}{\partial y}(\frac{\partial z}{\partial x}) = \frac{\partial}{\partial x}(\frac{\partial z}{\partial y}) [/itex]

Does that make any more sense now?

Is your equation meaning this ∂y/zx = ∂x/zy

any other help would be great becuase I am struggling to realise where to go next.

- #12

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You can't read that equation? It should read: ∂/∂y(∂z/∂x) = ∂/∂x(∂z/y)

- #13

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You can't read that equation? It should read: ∂/∂y(∂z/∂x) = ∂/∂x(∂z/y)

Thanks again.Is the next step now to bring the ∂z over to the other side and that is it complete?

- #14

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You don't seem to be familiar with taking partial derivatives, so heres a quick explanation:

∂z/∂x = the derivative of z with respect to x; treat y as if it were a constant (i.e. just a number). Simply take the x derivative like you would for dz/dx, if y was just some number.

∂z/∂y is exactly the same, just switch x and y in my instructions.

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