Question: Differentiation with the Leibniz notation.

Ive got new "problems" with my math book. This time it is about differentiating like Gottfried Wilhelm Leibniz (https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz), and his Leibniz notation.  (https://en.wikipedia.org/wiki/Leibniz%27s_notation).

dx/dy. Now that does sound like its just f'(x), of function f(x). But now they wanted something else i cannot produce. I could do the examples, and try to work it out like, but "im here to learn maple, not how to get my hands filthy with ink, and scratch on the paper when i make mistakes"... :P 

It says: Determine the differential that is being asked. 

No matter what i do, there wont be any solution that looks like the one given by the book. 

I would like to be good at this, while a lot of old books do still have the Leibniz notation. So it is eccential to be good at this if you want to really study the origins of math and science. 

Thank you!

Greetings,

The Function