Main Question or Discussion Point
I'm watching Susskind's Classical Mech. YouTube lecture series and am really confused about something he's doing where otherwise I've followed everything up until this point without a problem. In Lecture 3 he's dealing with the Euler-Lagrange equation applied to minimizing the distance between two points, and I understand his work up until here, where he starts taking the partial derivatives of the lagrangian with respect to v_i and v_i-1 rather than x_i. Why does he do this rather than continuing to take the derivatives w.r.t. x_i? He flatly says, "We're differentiating with respect to x-sub-i here" and then proceeds to take a partial derivative w.r.t. v_i and v_i-1 instead, I don't get it.