Let $T(x,y,z)=ln(e^{68}+x^2+y^2+z^2)$ correspond to the temperature in space, measured in degrees Fahrenheit.

$($a$).$ What is the directional derivative of $T$ at the origin in the direction of the vector $i+j+k?$

$($b$)$ What is the directional derivative of $T$ at the point $(1,1,1)$ in the direction to the origin?

$($c$)$ Assume a fly is flying with her path given by:

vec$(r)(t)=$

i$.$ Find the velocity of the fly when $t=1$ second.

ii$.$ Find the speed of the fly when $t=1$ second.

iii. What is the rate of change of temperature for the fly when $t=1$ second?