Since I was still struggling with the last related rates problem I posted, I thought I'd post a very simple one and I think that will help make my understanding of the topic better.

Each side of a square is increasing at a rate of 2 cm/s. At what rate is the area of the square increasing when the area of the square is 36 cm^2?

Now I know ds/dt is 2 and that I'm trying to find dA/dt. I also already know the solution, and how it came about, as it's in my notes, but I don't understand HOW the solution was derived. It basically ends up being dA/dt=2s*ds/dt but what I don't understand is WHY and HOW to get from knowing your given info, to knowing the equation you should be using to solve this problem is dA/dt=2s*ds/dt.