I don't understand how(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{\partial{f}}{\partial{x_k}}(\vec{a}) = \lim_{\epsilon\rightarrow 0} \frac{f(a_1,...,a_k+\epsilon,...,a_n)-f(a_1,...,a_k,...,a_n)}{\epsilon}[/tex]

can be equal to...

[tex]\Delta_k f = f(a_1,...,a_k + \epsilon,...,a_n)-f(a_1,...,a_k,...,a_n) \approx \Delta x_k \frac{\partial{f}}{\partial{x_k}}[/tex]

and why is it approximately?

what does [tex] \Delta x_k [/tex] really repersent? graphiclly and with an example.

why is

[tex] df = \sum \frac{\partial{f}}{\partial{x_i}} dx_i [/tex]

using [tex] dx_i [/tex] what does that graphicly represent? and what is Legendre transformation and what is its significance. Please try to explain (calc I-III, Linear algebra background)

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# Homework Help: Differentiation help

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