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I'm beginning to learn GR and ran across the following in the beginning of Stephani's book.

In deriving the equations of motion for a force-free particle, we have the Lagrangian:

[tex]L = \frac{m}{2} g_{\alpha \beta} \dot{x}^\alpha \dot{x}^\beta[/tex]

To construct the equations of motion we need

[tex]\frac{\partial L}{\partial \dot{x}^\nu} = m g_{\alpha \nu} \dot{x}^\alpha[/tex]

and

[tex]\frac{\partial L}{\partial x^\nu} = L_{,\nu} = \frac{m}{2} g_{\alpha \beta, \nu} \dot{x}^\alpha \dot{x}^\beta[/tex]

Then from the Lagrange equations we get

[tex]g_{\alpha \nu }\ddot{x}^\alpha + g_{\alpha \nu, \beta} \dot{x}^\alpha \dot{x}^\beta - \frac{1}{2}g_{\alpha \beta, \nu}\dot{x}^\alpha \dot{x}^\beta =0[/tex]

I don't understand where the second term in the last equation comes from.

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# Question about tensor derivative

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