I am making mess of the following expression..(adsbygoogle = window.adsbygoogle || []).push({});

i have following expression ## \frac{\partial{g}}{\partial{g_{\mu j}}} *g_{\nu j}=g \delta^{\mu} _{\nu} ##

then I have sum over j only in the above expression.

But above expression is nonzero only when ##{\mu}## is equal to ##\nu##.

So we have ## \frac{\partial{g}}{\partial{g_{\mu j}}} *g_{\mu j}=g ## ....(a)

I can understand that there is no ##\mu## dependence in right hand side so we have to sum over ##{\mu}## also. But doing the mathematical step just summing over ##{\nu}## gives equation in ##{\mu}## but in addition how the summation in that implied????

Also now if I take partial derivative of the above expression (a) how it gives

## \frac{\partial{g}}{\partial{g_{\mu j}}} *\frac{\partial{g_{\mu j}}}{\partial{x^{i}}}=\frac {\partial{g}}{\partial{x^{i}}} ##

?? why the term like ## \frac{\partial^{2}{g}}{{\partial{g_{\mu j}}}{\partial{x^{i}}}} ## vanishes???

please tell me what I am missing??

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# Little confused with tensor index manipulation

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