Hi. I have been looking at differential forms, and that inspired me to consider a partial derivative as a ratio between cross products. Please tell me if the following makes sense. Say we have cartesian coordinates (x,y) and polar coordinates ([itex]\rho[/itex], [itex]\phi[/itex]). I want to calculate [itex]\left(\frac{\partial x}{\partial y}\right)_{\rho}[/itex], i.e. the partial derivative of x wrt. y with [itex]\rho[/itex] constant. I do it as follows(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\left(\frac{\partial x}{\partial y}\right)_{\rho}=\left|\frac{\hat x\times\hat\rho}{\hat y\times\hat\rho}\right|=-\frac{\sin\phi}{\cos\phi}

[/tex]

Is this OK ? I've never encountered it before except in differential forms where I have seen partial derivatives written as wedge products.

Edit: This is the article I have been reading: http://www.av8n.com/physics/partial-derivative.htm#sec-freex

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# Connection between cross product and partial derivative

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