V(x, y, z) = 5x2 − 3xy + xyz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i + j − k.

Step-by-step explanation:

You have the following potential function:

          (1)

To find the rate of change of the potential at the point P(6,6,5) in the direction of v = i + j - k, you use the following formula:

          (2)

First, you calculate the gradient of V:

Next, you replace in the equation (2):

Then, the rate of change of the potential at the point P(6,6,5) in the direction of v, is 48.