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For example, the area of a square with side x is given by A=x

^{2}.

Then dA/dx can be computed and is equal to 2x.

The expression dA/dx=2x means the instantaneous change of A when x increases from a is 2a.

However, what is the meaning of dA=2xdx?

dA/dx is not a fraction, why is it valid to say dA=2xdx from the premise dA/dx=2x?

Furthermore, can anyone explain the same questions for dx=dA/2x?