Thread: gradient

This was confusing me so any help or step-by-step explanations would be appreciated!

Suppose the temperature at point (x,y,z) in space is given by the function
f(x,y,z) = 1/(1 + x^2 + y^2 + z^2)

An insect is located at the point P = (1,1,1) in space.

Find a direction (as a three-dimensional vector) in which the inital rate of change in the temperature is zero.

1)Find the gradient of that function.
2)Evaluate the gradient at (1,1,1).
3)Find what vector u needs to be so that the dot product between this vector and #2 is 0.

For solution see the attachment