Section 14.4: Tangent Planes

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