Question

Find the directional derivative of f at the given point in the direction indicated by the angle θ.

 

Answer 1

Step 1:

The function is , point is and angle is .

Consider .

Apply partial derivative on each side with respect to x.

Substitute in .

Apply partial derivative on each side with respect to y.

Substitute in .

Step 2:

The directional derivative in the direction of a unit vector then

.

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

.

Solution :

The directional derivative of the function is .