Relationship between Lagrangian and Energy

[theneedtoknow]

I know that, for time-independent potentials, we have E=sum (Vi*partial dL/dVi) - L
What if one or more of the potentials are time-dependent?
Is the relationship between energy and the lagrangian then "total dE/dt = - partial dL/dt "?

 

[dextercioby]

Yes.

 

[theneedtoknow]

Thank you! Would you happen to know of any textbooks where this is derived? I have the Landau and Lifgarbagez "Mechanics" one and they do not do so.