In the book Mathematical Methods for Physics and Engineering by Riley, Hobson, and Bence, I came across an equation I just can't seem to understand. In the chapter on tensors, they derive the equation for a Christoffel symbol of the second kind, [tex]\Gamma^{m}_{ij}=\frac{1}{2}g^{mk}\left(\frac{ \partial g_{jk}}{\partial u^{i}}+\frac{\partial g_{ki}}{\partial u^{j}}-\frac{\partial g_{ij}}{\partial u^k}\right)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Where the g's are the components of the metric tensor. I understood most of the derivation except for the part where they wrote, [tex] \frac{ \partial g_{ij}}{\partial u^{k}}= \frac{\partial e_{i}}{\partial u^{k}} \cdot e_{j}+e_{i} \cdot \frac{\partial e_{j}}{\partial u^{k}}[/tex]

Where the e's are the basis vectors. I just can't seem to understand how they got this equation.

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# Confusion about Christoffel Symbols

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