Why do we use dx when X is not a function?

Question

I know what a differential is, to the extent of Riemann sums. But when differentiating a function, say y=f(x), then oftentimes I see dy = f'(x)dx by the chain rule, which makes sense. But X isn't a function, it's the base variable, so how does it's derivative matter? On any case, if X is understood as the axis, wouldn't it's derivative simply be 1?

Answer 1

it's derivative is indeed 1.

Suppose you have $y=f(g(x))$.

where $f,\;g$ are differentiable, then by the chain rule:

$df=f'(g(x))g'(x)dx$

In this case: $g(x)=x, \;x'(x)=1$.