Dear old Leibnitz.
His notation is so convenient and flexible.
The main difficulty was typng the text, but no longer with modern computers or handwriting.
Writing f'(x) can be done on a single line. That was a good reason to introduce it.
Thank you for referring to Thomas & Finney (I have the 9th edition).
I think I have spotted your difficulty.
The differential defined on page 251 is dy, not dx
Using Leibnitz makes this more obvious