Read the following source carefully and answer the questions that follow:
The orders of the king
Thus speaks king Devanampiya Piyadassi: In the past, there were no arrangements for disposing affairs, nor for receiving regular reports. But I have made the following (arrangement). Pativedakas should report to me about the affairs of the people at all times, anywhere, whether I am eating, in the inner apartment, in the bedroom, in the cow pen, being carried (possibly in a palanquin), or in the garden. And I will dispose of the affairs of the people everywhere.
A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Find \( \frac{dS}{dx} \).