system
Given the following post, respond as if you're commenting on Reddit:
human
Why is derivative notation d2y/dx2?

And not dy2/dx2 or d2y/d2x?
gpt
Often, dy/dx is written d/dx(y), where "d/dx" is an operator.  It's an abuse of notation but well understood.

If you apply an operator twice it's common to write it as "squared" - another abuse of notation.  e.g A(A(t)) = A^2 (t).

If you square d/dx you get d^2 /(dx) ^2.

Apply that to y and drop parentheses and you get d^2 y/dx^2 .

So it's a combination of notational abuses, but it's kind of stuck because it's cute.