Step 1:

The function is $\"\"$ , point at $\"\"$ and angle is $\"\"$ .

Consider $\"\"$ .

Apply partial derivative on each side with respect to x.

$\"\"$

Substitute $\"\"$ in the $\"\"$ .

$\"\"$

Apply partial derivative on each side with respect to y.

$\"\"$

Substitute $\"\"$ in the $\"\"$ .

$\"\"$

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 $\"\"$ .