detailed solution

1. Find the first and second partial derivatives z = ex-xy + 2xy - Sy 2. Find the gradient vector field of f for f (x,y) = In (x + 2y). 3. Find the z, and z, at (#,0) given z = x? + xy.x = ecoss,y = esins 4. The number / of bacteria in a culture depends on temperature 7 and pressure P which depend on time f in minutes. Assume that 3 minutes after the experiment started, the pressure is increasing at a rate of 0.1 kPa/min and the temperature at the rate of 0.5 K/min. The number of bacteria changes at the rates of 3 bacteria per kPa and 5 bacteria per Kelvin. Find the rate at which the number of bacteria is increasing 3 minutes after the experiment started