21. The previous derivatives are consistent with the energy operator, corresponding to the time derivative , 22. Then the two terms which contain time derivatives can be combined into a single term. 23. Let \ dot { x } denote the time derivative of the constant mode x. 24. Another result from the Legendre transformation relates the time derivatives of the Lagrangian and Hamiltonian: 25. Where the dot represents a time derivative . 26. The above inner product can also be written in terms of and its time derivative . 27. And taking the total time derivative of the second equation and equating to the first. 28. The remaining 3 Einstein equations contain only first order time derivatives of the metric tensor. 29. When talking about a time derivative , a better analogy would be velocity and acceleration. 30. This wave equation incorporates fractional time derivatives :
