$[$C$]$ Suppose that the temperature at the point $(x,y,z)$ in space is given by $T(x,y,z)$ degrees Celsius. An object is moving through space in such a way that its $x-$ and $y-$coordinates both increase at a rate of $2$ meters per second and its $z-$coordinate decreases at a rate of $5$ meters per second. If the object is a location where $\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{x}}=6,\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{y}}=8,$ and $\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{x}}=3($each with units degrees Celsius per meter$),$ use a Chain Rule to calculate $\frac{dr}{dt}$ in order to determine the rate a which the object's observed temperature of space is changing as it moves, when it is at the location described above. Include appropriate units in your answer.