- #1

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What I want to understand is the interpretation of the theorem and specifically a visualisation of why what the theorem states must be the case.

My guess is that this theorem is saying that change is symmetrical. But I don't know if this is only true for second derivatives.

If you don't know this theorem by its name the theorem basically says this:

∂/∂y(∂f/∂x)=∂/∂x(∂f/∂y)

Also, I would like to know if you consider my focus on visualisation to be not worthwhile and that I should instead just trust this theorem.

I thank you in advance.