The temperature at a point $(x,y)$ on a flat metal plate is given by $T(x,y)=\frac{41}{9x^2{y}^2},$ where $T$ is measured in $C$ and $x,y$ in meters. Find the rate of change of temperature with respect to distance at the point $(2,2)$ in the $x-$direction and the $y-$direction.

$($a$)$ the $x-$direction

$\frac{C}{m}$

$($b$)$ the $y-$direction

$\frac{C}{m}$