$\"\"$

\

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 $\"\"$ .

\

$\"\"$

\

$\"\"$

\

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

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .