Suppose the Formula for Wind Chill C (In Degrees Fahrenheit) $C = 37.05 + 0.6844 T - 37.59 v ^ { 0.16 } + 0.4425 T v ^ { 0.16 }$

Suppose the formula for wind chill C (in degrees Fahrenheit) is given by $C = 37.05 + 0.6844 T - 37.59 v ^ { 0.16 } + 0.4425 T v ^ { 0.16 }$ where $v$ is the wind speed in miles per hour and $T$ is the temperature in degrees Fahrenheit. The wind speed is $23 \pm 3$ miles per hour and the temperature is $8 ^ { \circ } \pm 1 ^ { \circ }$ Fahrenheit. Use $d C$ to estimate the relative error in calculating the wind chill. Round your answer to two decimal places.

A) $\frac { d C } { C } = \pm 12.62$
B) $\frac { d C } { C } = \pm 17.81$
C) $\frac { d C ^ { + } } { C } = \pm 12.81$
D) $\frac { d C } { C ^ { c } } = \pm 12.62$
E) $\frac { d C } { C } = \pm 0.19$