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.