- #1

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- 5

## Main Question or Discussion Point

often times you will see naive people cancel differentials to obtain whatever it is they want for example :

[tex] \frac{dx}{dy} \frac{dy}{dz} = \frac{dx}{dz} [/tex]

now i know this isn't rigorous and my question is actually about partials. is there ever an occassion/space/set/etc where i can do this:

[tex] \frac{\partial x}{\partial y} \frac{\partial x}{\partial z} = \frac{ \partial^2 x}{\partial y \partial z}[/tex]

[tex] \frac{dx}{dy} \frac{dy}{dz} = \frac{dx}{dz} [/tex]

now i know this isn't rigorous and my question is actually about partials. is there ever an occassion/space/set/etc where i can do this:

[tex] \frac{\partial x}{\partial y} \frac{\partial x}{\partial z} = \frac{ \partial^2 x}{\partial y \partial z}[/tex]