We are given a coordinate $x$ and a function $f(x)$ at each point on $x$. We need to compute the derivative at a point $x$. For this, we usually choose two points $x+dx$ and $x$ (first principles). Can we also choose the points $x-dx$ and $x$ and get the same derivative?
If not, why?
If yes, why do we get opposite values for directional derivatives in two opposite directions?