Since I have studied the derivative in advanced mathematics, I should know that it is also called "WeChat Quotient", because dy is differential, dx is differential, and both are division (actually related to the limit, but in terms of expression). High school mathematics only learned the geometric meaning of derivatives and some commonly used formulas for derivation, while advanced mathematics (more accurately, calculus or differential calculus) involved deeper and wider.

What you said "D is derivative" is incorrect, which means "differential" or "infinitesimal increment". For example, dy represents the differential of y, or represents the tiny increment of y at a certain value (usually considered as infinitesimal). When dealing with some problems, we often encounter the "infinitesimal method", and there will be various quantities expressed by D, such as a certain time infinitesimal for dt, a certain mass infinitesimal for dm and so on.

Regarding the expression of the second derivative, it is suggested that the textbook or the teacher should prevail, and you will naturally understand it after reading more relevant introductions and discussions.

For reference only.