(8.23) states:
\[ \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q}} \right) - \frac{\partial L}{\partial q} = 0 \]
To show that Eq. (8.24) follows from Eq. (8.23), we need to manipulate Eq. (8.23) to obtain Eq. (8.24).
Eq. (8.24) states:
\[ \frac{d}{dt}
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