Chapter 14.4, Problem 46E

The wind-chill index is modeled by the function $W=13.12+0.6215T-11.37v^{0.16}+0.3965T{v}^{0.16}$ where $T$ is the actual temperature (in ${}^{°}\text{C}$ ) and $v$ is the wind speed (in $\text{km}/\text{h}$ ). The wind speed is measured as $26 \text{km}/\text{h}$ , with a possible error of $\pm 2 \text{km}/\text{h}$ , and the actual temperature is measured as $-{11}^{°}\text{C}$ , with a possible error of $\pm 1^{°}\text{C}$ . Use differentials to estimate the maximum error in the calculated value of $W$ due to the measurement errors in $T$ and $v$ .