Step 1:

The function is , point is  and vector is .

(a)

Find gradient of .

The gradient of the function is the vector function of , then .

Consider .

Apply partial derivative on each side with respect to .

Apply partial derivative on each side with respect to .

Then the gradient vector of is .

Step 2:

(b)

Find the gradient vector at a point .

Substitute in the gradient vector.

The gradient vector at a point is .

Step 3:

(c)

The rate of change of the function in the direction of a vector u is .

The vector and a point is .

The rate of change of the function at a point in the direction of a vector u is

Solution :

(a) .

(b) .

(c) .