Suppose there is a spaceship in three-dimensional space, with our sun located at the origin, (0,0,0). The temperature near the sun is extremely hot, of course -- about 6000K -- and it drops rapidly as one moves away. Suppose the temperate at any point is space is given by T(x,y,z)=6000/(1+(x^2+y^2+z^2)/5), where x, y, and z measured in units of 10 million miles. (Here we're assuming the spaceship will never get close enough to other stars to notice their heat, so effectively our sun is the only heat-producer in the universe.)

Suppose now that the spaceship is located on the Earth, about 93 million miles away, at the point (9,2,1). What is the directional derivative (change in K per change in position) if the spaceship were to move in the direction of the vector (-4,-3,5)?