The temperature at a point $($x$,$y$)$ on a rectangular metal plate is given by

T$($x$,$y$)=100/(5$x$^2+$ y$^2)$

$($a$)$Find the rate of change of T at the point $(6,7)$ in the direction of the vector $(3,4)$

$($b$)$At the point $(6,7),$ find a unit vector in the direction in which the temperature increases the fastest.

$($c$)$What is the maximum rate of change of T at the point $(6,7)?$