Before we go taking derivatives and finding rates, let\'s first relate pressure, volume, and temperature. If you know chemistry well, those values should immediately suggest the combined gas law: PV / T = C, where P represents pressure, V represents volume, T represents temperature, and C represents some arbitrary constant. Now, we can take the natural logarithms of both sides of this equation: ln (PV / T) = ln C Using the properties of logarithms (specifically, the properties that the logarithm of a product is the sum of the logarithms, and that the logarithm of a quotient is the difference of the logarithms): ln P + ln V - ln T = ln C We want to eventually find an expression for the rate of change of pressure, so let\'s isolate the pressure in this equation by putting all terms containing P on one side and all terms not containing P on the other: ln P = ln T - ln V + ln C Now we can take derivatives, using the sum and difference rules for derivatives, to find an appropriate formula for the rate of change of pressure (notice that the constant term, which remains unaffected by time, has a derivative of 0 with respect to time): d (ln P) / dt = (d (ln T) / dt) - (d (ln V) / dt) Solution Before we go taking derivatives and finding rates, let\'s first relate pressure, volume, and temperature. If you know chemistry well, those values should immediately suggest the combined gas law: PV / T = C, where P represents pressure, V represents volume, T represents temperature, and C represents some arbitrary constant. Now, we can take the natural logarithms of both sides of this equation: ln (PV / T) = ln C Using the properties of logarithms (specifically, the properties that the logarithm of a product is the sum of the logarithms, and that the logarithm of a quotient is the difference of the logarithms): ln P + ln V - ln T = ln C We want to eventually find an expression for the rate of change of pressure, so let\'s isolate the pressure in this equation by putting all terms containing P on one side and all terms not containing P on the other: ln P = ln T - ln V + ln C Now we can take derivatives, using the sum and difference rules for derivatives, to find an appropriate formula for the rate of change of pressure (notice that the constant term, which remains unaffected by time, has a derivative of 0 with respect to time): d (ln P) / dt = (d (ln T) / dt) - (d (ln V) / dt).