Ex 14.4.5 Use the chain rule to compute z/x and z/y for 2x + 3y - 2z = 9. (answer) Ex 14.4.6 Use the chain rule to compute z/x and z/y for 2x + y + z = 9. (answer) Ex 14.4.7 Use the chain rule to compute z/x and z/y for xy + 2 = 5. (answer) Ex 14.4.8 Use the chain rule to compute z/x and z/y for 2 sin(xyz) = = 1. (answer) Ex 14.4.9 Chemistry students will recognize the ideal gas law, given by PV = nRT which relates the Pressure, Volume, and Temperature of n moles of gas. (R is the ideal gas constant). Thus, we can view pressure, volume, and temperature as variables, each one dependent on the other two. a. If pressure of a gas is increasing at a rate of 0.2Pa/min and temperature is increasing at a rate of 1K/min, how fast is the volume changing? b. If the volume of a gas is decreasing at a rate of 0.3m/min and temperature is increasing at a rate of .5K/min, how fast is the pressure changing? c. If the pressure of a gas is decreasing at a rate of 0.4Pa/min and the volume is increasing at a rate of 3L/min, how fast is the temperature changing?