31. It is agreed that time derivatives are taken with respect to the proper time \ tau. 32. Equations ( ) and ( ) allow us to eliminate the time derivatives of \ theta. 33. Where " i " times the time derivative is the Hamiltonian operator in quantum mechanics. 34. Where in this context the overdot denotes a partial time derivative , not a total time derivative. 35. Where in this context the overdot denotes a partial time derivative, not a total time derivative . 36. The time derivative of the energy density ( using the product rule for vector dot products ) is 37. If the rotation matrix is time dependent, then it does not commute with the time derivative . 38. Consider the time derivative of ( 2 ), which we can compute using the chain rule, 39. The total time derivative denoted d / d " t " often involves implicit differentiation. 40. This velocity can be computed by taking the time derivative of the position of the center of mass.
