Implicit differentiation Question

https://www.quora.com/profile/Bravewarrior/p-153075726
Here is the question with its solution. I basically do not understand what they have done in the solution, and how the product rule has even been used here. Some help would be greatly appreciated!

Its a simple example of the product rule for
x*y(x)
so f(x)=x and g(x)=y(x) ...

hey,

do you understand how the product rule works? if not, probably look back on that first!

i personally tackle the product rule in a different way to how they did it here, so i'll try to explain my method and hopefully it'll help you understand theirs:

i let u = x so du/dx = 1
then i let v = y, so dv/dx = dy/dx

the product rule formula is: u(dv/dx) + v(du/dx)

since we don't know what y actually is we have to just say its differential is dy/dx. in many questions they ask you to rearrange to get this answer.

i hope this helps!