Basically y is a function, so each time we differentiate y, we get dy/dx

Any term involving d/dx (y) will become dy/dx

All this while, in the O Levels last year, you have been doing the differentiation with y on one side and everything else in x on the other side.

This "implicit differentiation" extends this to any general function in which y does not have to be made the subject before performing dy/dx.

You will see in this chapter that the notation "d/dx (...)" will be used very commonly here.

Is this some poly calculus course?

nopee, but the module is calculus. im in a chemical engineering course