I am not quite sure how [tex]\frac{\partial}{\partial u}\left(\frac{\partial z}{\partial u}\right)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]=\frac{\partial}{\partial u}\left( u \frac{\partial z}{\partial x}+v\frac{\partial z}{\partial y} \right)[/tex]

comes to [tex]\frac{\partial z}{\partial x} + u\frac{\partial}{\partial u}\left(\frac{\partial z}{\partial x}\right)+v \frac{\partial}{\partial u}\left(\frac{\partial z}{\partial y}\right)[/tex]...

I would have evaluated this to be the same but without the [itex]\frac{\partial z}{\partial x}[/itex] term. i.e.:

[tex]u\frac{\partial}{\partial u}\left(\frac{\partial z}{\partial x}\right)+v \frac{\partial}{\partial u}\left(\frac{\partial z}{\partial y}\right)[/tex]

I know I am probably overlooking something obvious/simple but I can't see what it is. Could anyone tell me?

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# Partial Differentiation: second partial derivative

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