An atmospheric pressure field is given as P(x, y, z) = (x - 2)2 + (y - 2)2 + (z + 1)2, where the xy plane is parallel to the surface of the ocean and the z direction is vertical. Find:
(a) The magnitude and direction of the pressure gradient.
(b) The derivative of the pressure in the vertical direction.
(c) The derivative of pressure in the direction parallel to the surface, at 45° between the positive x and y axes.