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I'm not sure whether to say evaluate or solve. Should the result be something like, $zx + xy + c(y,z) = 0$ or shall I ignore $c(y,z)$?

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    Correct, and then from the chain rule you know that this is zero if $\frac{\partial x}{\partial y}=0$ and $\frac{\partial x}{\partial z}=0$. If only one of them is zero, you will have c(y) or c(z), and if both are zero you will have a regular old constant number. I'd post this as an answer, but I've not actually done multi-variable calculus and so there might be something I'm missing. To the best of my knowledge, though, that's your answer.2012-11-06

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