In thermodynamics, it is frequently said that work and heat are path functions with inexact differentials $\delta Q$, $\delta W$, so one can not talk about a change in work or a change in heat since they are not state properties of the system. If so, why do I usually find power defined as the derivative of work with respect to time if work is not a function and we can not speak about changes in work ?
And in general if work is $W = \int_C{\textbf{F}}^{}\cdot d\textbf{x}$, how can we evaluate $P(t)=\frac{d W}{dt}$?