  The partial derivative of the kinetic energy of a dynamical system with
respect to a generalized coordinate as it appears in the Lagrangian formalism
is not equal to the derivative of the kinetic energy with respect to the same
coordinate in the Hamiltonian formalism but differs by a sign. We find another
exact relation between the two partial derivatives in the case of a
conservative system. We also identify another form of kinetic energy whose
partial derivative with respect to a generalized coordinate vanishes
identically.
