The temperature at (x, y, z) of a solid sphere centered at the origin is T(x, y, z) = e^-(x² + y²+z²).
(1) Find the directional derivative of T at (1,1,-1) in the direction of = (1,2,2). (2) In which direction at (1, 1,-1), the temperature increases most rapidly? Find the maximum rate of change.