Say, E is dependent to x,y,z. I'm expecting it's derivative at [tex]x_0,y_0,z_0[/tex] to be(adsbygoogle = window.adsbygoogle || []).push({});

[tex]dE = \lim_{\substack{\Delta x\rightarrow 0\\\Delta y\rightarrow 0\\\Delta z\rightarrow 0}} E(x_0+\Delta x, y_0+\Delta y,z_0+\Delta z) - E(x_0,y_0,z_0)[/tex]

But with following definition, it's not the thing above:

[tex]dE = \lim_{\substack{\Delta x\rightarrow 0\\\Delta y\rightarrow 0\\\Delta z\rightarrow 0}} \frac{E(x_0+\Delta x, y_0,z_0) - E(x_0,y_0,z_0)}{\Delta x} \Delta x + \frac{E(x_0, y_0+\Delta y,z_0) - E(x_0,y_0,z_0)}{\Delta y} \Delta y + \frac{E(x_0, y_0,z_0+\Delta z) - E(x_0,y_0,z_0)}{\Delta z} \Delta z = \frac{\partial E}{\partial x}dx + \frac{\partial E}{\partial y}dy + \frac{\partial E}{\partial z}dz[/tex].

Now, which is correct? (and why?!?)

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# Partial differentiation

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