Okay so this one I thought was going to be more straight forward because I was given an equation that relates that which dependent upon time t.

when a certain gas expands or contracts adiabatically, it obeys the law $\displaystyle PV^1.4 = K$ where P is pressure, V is volume and K is a constant.

At a certain instant the pressure is 40 N/cm^2, the volume is 32cm^3, and the volume is increasing at a rate of 5 cm^3 per second. At what rate is the pressure changing at this instant.

So I thought the given equation was the one I would use. I solve it to find K

$\displaystyle 40(32^1.4) = 5120$

then I differentiated the equation

$\displaystyle \frac{d}{dt} [PV^1.4=k] \Rightarrow V^1.4\frac{dP}{dt} + (1.4V^.4)P\frac{dV}{dt} = 0$

I can't figure out how to make exponents with decimal points work in latex.. the exponents are 1.4 and .4 after the differentiation.

anyway, Am I on the right track?