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What's the derivative of E (below equation) partial to w: ( consider that w is vector) enter image description here

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Just compute the derivative with respect to each component $w_j$. This will give you a vector which is your solution. –  Matt L. Apr 12 '13 at 7:15
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up vote 1 down vote accepted

For each $k \in \{0,1,\ldots,M\}$:

$$\frac{\partial E}{\partial w_k} = \sum_{n=1}^N x_n^k\, x_n^i = 0$$

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thank you very much –  zhilevan Apr 12 '13 at 8:07
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