Step 1:

Two cars are start moving from the same point.

Let south one $\"\"$ and west one $\"\"$ and distance between them $\"\"$ .

one car travels south at $\"\"$ and other one travels west at $\"\"$ .

Means that : $\"\"$ .

Draw a right triangle for the given data :

$\"\"$

After two hours,

$\"\"$ and $\"\"$ .

Solve $\"\"$ by using Pythagorean theorem.

$\"\"$

Find $\"\"$ by differentiating $\"\"$ with respect to $\"\"$ .

$\"\"$

Substitute corresponding values in above equation.

$\"\"$