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 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

then I differentiated the equation

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?