When can I do the following where ##h_{i}## is a function of ##(x_{1},...,x_{n})##?(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{\partial}{\partial x_{k}}\frac{\partial f(h_{1},...,h_{n})}{\partial h_{m}}\overset{?}{=}\frac{\partial}{\partial h_{m}}\frac{\partial f(h_{1},...,h_{n})}{\partial x_{m}}\overset{\underbrace{chain\ rule}}{=}\frac{\partial}{\partial h_{m}} \sum_{l=1}^{n} \frac{\partial f(h_{1},...,h_{n})}{\partial h_{l}}\frac{\partial h_{l}}{\partial x_{k}}[/itex]

And why? Thank you for your time.

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# Symmetry in second order partial derivatives and chain rule

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