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Precise meaning of dA=2xdx

lamsung

New member
Jul 19, 2013
5
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

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
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<<.