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[tex]S = \int L(q,\dot{q},t) \,dt[/tex]

The variation is:

[tex]\delta S = \int \left(\frac{\partial L}{\partial q}\delta q+\frac{\partial L}{\partial \dot{q}}\delta\dot{q}\right)\,dt[/tex]

I'm guessing this is some type of chain rule, but I haven't been able to derive it... how is it justified?

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# Variation of the lagrangian

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