Lagrangian: How did they get from this step to the other?

[unscientific]

Homework Statement

Homework Equations

The Attempt at a Solution

I don't understand where the third term from the first equation of 5.192 come about.. as clearly L doesn't depend on x at all, so ∂L/∂x should be zero.

 

[Chopin]

The second and third terms both come from differentiating the $m\ell\dot{\theta}\cos{\theta}$ term...you get two terms because there are two $\theta$'s in it.

 

[unscientific]

The second and third terms both come from differentiating the $m\ell\dot{\theta}\cos{\theta}$ term...you get two terms because there are two $\theta$'s in it.

ah that makes sense! thanks a lot!