In school I was taught that we use dudx as a notation for the first derivative of a function u(x). I was also told that we could use the d just like any variable.
After some time we were given the notation for the second derivative and it was explained as follows:
d(dudx)dx=d2udx2
What I do not get here is, if we can use the d as any variable, I would get the following result:
d(dudx)dx=ddudxdx=d2ud2x2
Apparently it is not the same as the notation we were given. A d is missing.
I have done some research on this and found some vague comments about "There are reasons for that, but you do not need to know..." or "That is mainly a notation issue, but you do not need to know further."
So what I am asking for is: Is this really just a notation thing?
If so, does this mean we can actually NOT use d like a variable?
If not, where does the d go?
I found this related question, but it does not really answer my specific question. So I would not see it as a duplicate, but correct me if my search has not been sufficient and there indeed is a similar question out there already.
