please solve the following question in detail

2. The temperature (in degrees Celsius) at a point (x, y, 2) inside a metal rod is given by: xyz 1+x2+y2+z2 T(x, y, z) = (a) Find the rate of change of temperature with respect to distance at (1, 1, 1) in the direction of the origin. (b) Find the direction in which the tbmperature rises most rapidly at the point (1, 1, 1). Express your answer as a unit vector. (c) Find the rate at which the temperature rises moving om (1, 1, 1) in the direction obtained in part (b)