Question

What is the difference between delta x and dx? Thank you in advance.

Answer 1

`delta x` is generally used to represent a small (but finite) increment in its associated variable `x`.

E.g. This is used in the formal definition of the derivative:

`lim_(delta x rarr 0) (f(x+deltax) - f(x))/(delta x)`

Whereas `dx` represents "with respect to" when used in a differential or an integral.

E.g. `d/dx (x^2+2x)`, or `dy/dx`, or `int pi \ y^2 \ dx`

In this context the `dx` is actually part of an operator, and no longer represents a small finite increment.

The terminology is very often misused, especially by physicists, who might state something like, "we add up add the `dx`'s. But in formal mathematics such a statement is nonsense.

If we look at the chain rule, we can write:

`dy/dx = dy/dt * dt/dx`

And it appears that the `dt`'s cancel, and indeed we could write:

`dy/dx = dy/(cancel(dt)) * cancel(dt)/dx`

But it is important to realise that although this "cancellation" property holds that `dx` (or `dt`) is just part of the notation (hence the reason the notation is used) and is not a finite fraction the can be cancelled.