As a linear approximation tool, differentials are perfectly understandable. When we write dy = f’(x) $Delta$x, the "f’(x)" is just a fixed quantity ( the derivative of the function “f” at a specific point “x”). A definition problem arises when we use them with the Leibniz notation for integrals or with differential equations (as in the “separation of variables” method).
When we write "dy = f’(x) dx", that cannot be a definition (because of the “d” notation on both sides) and it is not a limit either (when $Delta$x goes to zero), because such limit is obviously zero.

Question

As a linear approximation tool, differentials are perfectly understandable. When we write dy = f’(x) $Delta$x, the "f’(x)" is just a fixed quantity ( the derivative of the function “f” at a specific point “x”).  A definition problem arises when we use them with the Leibniz notation for integrals or with differential equations (as in the “separation of variables” method).
When we write "dy = f’(x) dx", that cannot be a definition (because of the “d” notation on both sides) and it is not a limit either (when $Delta$x goes to zero), because such limit is obviously zero.

anonymous · Answer

Ops... the equation button is not working... Where's the greek letter "Delta"?