so i know for example that d/dt (∂L/∂x*i) = ∂L/∂xi for cartesian coordinates, where xi is the ith coordinate in Rn and x*i is the derivative of the ith coordinate xi with respect to time. L represents the lagrangian. so using an arbitrary change of coordinates, qi = qi(x1, x2, ..., xn) i have that ∂L/∂x_i = ∂L/∂qi * ∂q_i/∂x_i and that ∂L/∂x*i = ∂L/∂q*i * ∂q*i/∂x*i and substituting i get: d/dt(∂L/∂q*i * ∂q*i/∂x*i) = ∂L/∂qi * ∂qi/∂xi and using the product rule i get: d/dt(∂L/∂q*i) * ∂q*i/∂x*i+ ∂L/∂q*i * d/dt(∂q*i/∂x*i) = ∂L/∂qi* ∂qi/∂xi using the fact that ∂q*i/∂x*i = ∂qi/∂xi, d/dt(∂L/∂q*i) * ∂qi/∂xi + ∂L/∂q*i * d/dt(∂qi/∂xi) = d/dt(∂L/∂q*i) * ∂qi/∂xi + ∂L/∂q*i * (∂q*i/∂xi) = d/dt(∂L/∂q*i) * ∂qi/∂xi+ ∂L/∂xi = ∂L/∂qi * ∂qi/∂xi. if i didn't have that ∂L/∂xi on the left side then i could just cancel out the ∂qi/∂xi on both sides and i would be done. have i made a mistake somewhere or am i missing something? thanks.