dEdt

dEdt is a shorthand commonly used to denote the time derivative of energy, written mathematically as dE/dt. It expresses how the energy E of a system changes as time t progresses. When E is a function of time, E = E(t), the derivative dE/dt measures the instantaneous rate of change of energy.

In physics and engineering, dE/dt is interpreted as a rate of energy transfer or conversion, and is closely related to power. If E is measured in joules, then dE/dt has units of joules per second, or watts. A positive dE/dt means the system is gaining energy, while a negative value signifies energy loss.

The meaning of dE/dt depends on the chosen definition of E. In mechanical systems, E may be the total mechanical energy (kinetic plus potential). In thermodynamics, E could represent internal energy, and dE/dt can relate to heat flow and work through the relation dU/dt = δQ/dt − δW/dt for the internal energy U. In electrical circuits, E might denote stored electrical energy in capacitors or inductors, and dE/dt corresponds to the instantaneous power supplied or delivered by sources.

Notationally, dEdt is sometimes used in informal notes or inline text to emphasize the derivative of E with respect to t, but the standard mathematical form is dE/dt. In discrete-time analyses, the derivative is approximated by ΔE/Δt.

Overall, dEdt (or dE/dt) is a fundamental measure of how energy evolves in time within a system, reflecting the balance of energy inputs, outputs, and losses.