Question

Find the directional derivative of the function at the given point in the direction of the vector v.

Answer 1

Step 1:

The function is , point is and vector is .

The directional derivative of the function in the direction of a unit vector is

.

Consider .

Apply partial derivative on each side with respect to .

Substitute in .

Apply partial derivative on each side with respect to .

Substitute in .

Step 2:

Here v is not a unit vector, but unit vector u is in the direction of v is .

The directional derivative of the function at a point in the direction of a unit vector is

.

Solution :

.