I am a graduate student in the economics department. I should write a dissertation. I got stuck in an equation. There is an equation like this ($\ln P = \ln K + \ln W - \ln Q$). All the variables have a unique meaning. But the K variable is the most important. I want to say that the change rate of K is 0. Is it possible to say that to illustrate the rate of the difference all the variables' we should take derivatives like this ($dP/P = dK/K + dW/W - dQ/Q$). If so I can say $dK/K = 0$.
edit: P: Price K: Fixed mark-up rate C: Unit labor costs P = K.C Unit labor cost is W/C and W is the hourly wage of labor C = W/Q So P = K.(W/Q) I want to illustrate the impact of the dependent variables on the independent variable. But the mark-up rate is unchangeable. All the rest variables are time-dependent. I guess I should differentiate the equation with respect to time. Is my way true?
If $K,W,Q$ are univariate functions of time, with $P$ determined by $K,W,Q$ , then indeed one may differentiate w.r.t time:
$$\dot P/P=\dot K/K+\dot W/W-\dot Q/Q$$
and what you wrote is just differential notation for the above.