Activity $2\mathrm{.}5\mathrm{.}4.$

Activity $2\mathrm{.}5\mathrm{.}4.$ Use known derivative rules, including the chain rule, as needed to answer each of the following questions.

c$.$ At sea level, air pressure is $30$ inches of mercury. At an altitude of $h$ feet above sea level, the air pressure, $P,$ in inches of mercury, is given by the function $P=30e^{-0\mathrm{.}0000323h},$ Compute $d\frac{P}{d}h$ and explain what this derivative function tells you about air pressure, including a discussion of the units on $d\frac{P}{d}h.$ In addition, determine how fast the air pressure is changing for a pilot of a small plane passing through an altitude of $1000$ feet.