If f is a function and x is a variable then dx means that you should express f with respect to an input x, so if A is the area of a a circle then what is dA?

If f is a function and x is a variable then dx means that you should express f with respect to an input x, so if A is the area of a a circle then what is dA? since A = pir^2 you have that dA = 2pirdr since A = pi(l/(2pi))^2 where l is the perimeter then you have dA = pi2(l/(2pi))(1/(2pi))dl, so the idea of dA is something related to the diferential of the variable used to define A. The use of the chain rule allow us to operate with differentials. For example, since here r = l/(2pi) we have that dr = dl/(2pi) so that dA = 2pirdr = 2pi(l/(2pi))dl/(2pi) = 1/(2pi)ldl. An finally this implies that dA/dl = 1/(2pi)l