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show that if $$f(x, y, z)=0$$ then $$\left ( \partial x \over \partial y \right )_{z}\left ( \partial y \over \partial z \right )_{x}\left ( \partial z \over \partial x \right )_{y}=-1$$

I don't know how to tackle this problem although I've tried.

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  • $\begingroup$ Could you show your working then? There are many proofs of this online, but if you have your working and are stuck on a certain step, we can better help you. $\endgroup$ – Toby Mak Sep 19 '19 at 10:25
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I could write it all out, but I think that what you are referring about is the triple product rule. A derivation can be found on:

https://en.wikipedia.org/wiki/Triple_product_rule

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