So I have started a 3rd calculus class and my prof uses primarily leibniz notation. (Ex.

) and I don't really understand how it all works.

Like I get that when you write dy/dx it's basically the difference between x and y as that difference gets arbitrarily small.

I also understand that in an integral, the dx stands for a tiny verticle sliver and the integral means we are adding up an infinite number of those slivers.

I get lost after that. For example, how does the chain rule use this notation? I've heard there are benefits to it in explaining the chain rule, but I don't quite follow it. An example/explanation would be great.

Finally I am given equations such as:

for the arclength of a function and:

for the arclenth of a function given using a parametric equation.

So what do these mean? In the first one, what would I replace dx and dy with. How about in the second one, what is (dx/dt)?

Thanks in advance,

-Keilan