What is the Precise Meaning of dA=2xdx?

[lamsung]

Every equation has a meaning.

For example, the area of a square with side x is given by A=x².

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?

 

[Sudharaka]

Every equation has a meaning.

For example, the area of a square with side x is given by A=x².

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?

Hi lamsung, :)

Welcome to MHB! (Handshake)

The derivative and the differential can be separately defined and there are several approaches to define the differential precisely. You would find those definitions >>here<<. However a more simple (and less precise) definition for the differential can be found >>here<<.