x represents the side length of the square ... the problem states that the edge (side) isexpanding at a rate of 2 cm/sec... x is changing over time and represents that rate of change ... it's symbology can be read as "the rate that x changes w/r to time".

since x is an implicit function of time, then , and because of the chain rule

I recommend you review your previous lessons in finding implicit derivatives. The mechanics of taking derivatives are the same in this situation.