Refer to Table 8.5 shown below giving the heat index, I, in ◦F, as a function f(H, T) of the relative humidity, H, and the temperature, T, in ◦F. The heat index is a temperature which tells you how hot it feels as a result of the combination of humidity and temperature.
Estimate ∂I∕∂H and ∂I∕∂T for typical weather conditions in Tucson in summer (H = 10, T = 100). What do your answers mean in practical terms for the residents of Tucson?

Table 8.5 Heat index (◦F)

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Humidity |0 1020 30 40 501 60 8888850 70 64 65 75 69 70 66 67 68 74 72 73 69 75 70 76 80 73 75 77 78 791 82 85 73 8032848638 90 81 78 Temperature (°F) 90 83 85 87 90 93 96 100 humidity (%) 95 100 105 87 91 95 90 95 100 93 99 105 104 113 123 120 135 149 101 110 107 114 132 110 115 99 103 105 111 112 120 123 135 137 151 150