I am wroking through an electrodynamics textbook and there is this Taylor expansion to do later a multipole expansion. But I can't figure out how the author does it. Please any help?(adsbygoogle = window.adsbygoogle || []).push({});

the expansion:

[tex] \frac{1}{|\vec{r}-\vec{r'}|} = \frac{1}{r} - \sum^3_{i=1} x'_i \frac{\partial}{\partial x_i} \frac{1}{r} + \frac{1}{2} \sum^3_{i,j=1} x'_i x'_j \frac{\partial}{\partial x_i} \frac{\partial}{\partial x_j}\frac{1}{r} + \mathellipsis [/tex]

And he writes "the occuring differenciations were changed using:"

[tex] (\frac{\partial}{\partial x'_i} \frac{1}{|\vec{r}-\vec{r'}|})_{r'=0} = - (\frac{\partial}{\partial x_i} \frac{1}{|\vec{r}-\vec{r'}|})_{r'=0} = - \frac{\partial}{\partial x_i} \frac{1}{r} [/tex]

I just can't follow his argument..

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# Taylor expansion of 1/|r-r'|

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