system
Given the following post, respond as if you're commenting on Reddit:
human
Is deriving symetric?

Usually derivation is explained like how the function changed when the variable changed. The way we do it is comparing the current point with a close previous one. 
(f(x)-f(x-h))/h with small h
My question here is, can we compare the current point with the close next one? Like doing a mirror at x
(f(x+h)-f(x))/h with small h
I did a few tries with simple functions and it's working and makes sense but I don't know if it's something general or not.
gpt
You are describing taking the limit from the left (x-h is left of x on the number line) compared to taking the limit from the right (x+h is right of x on the number line).  THE limit is defined to exist when the limits from the left and right are equal, and there is no limit when the two directional limits disagree.  So if there is a limit to something, you can use either method to computer it.

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Consider f(x)=|x|/x as x->0.  The limit from the right goes to +1, while the limit from the left goes to -1, so there is no limit.  Compare that to g(x)=(|x|/x)^2, where both directional limits go to 1, so here the limit exists and you are free to computer it from either direction.

Edit:  If you're doing "standard" math stuff like in high school, you might have to think hard to come up with many cases where the limits disagree, so you are usually safe to use either method.