Usually when you start to take derivatives you begin with equations that say
y = ……..
You see y on the left side of the equation, but only once and by itself. And at first there is generally just one variable on the right side of the equation.
You can however find the derivative of an equation if y is not isolated and if y has other operations being done upon it. The variable y may also show up more than once. The chain rule is required.
Again, you definitely want to remember the chain rule when you do implicit differentiation!
Later on you will solve for dy/dx or dz/dx or whichever term you are trying to find.
dy/dx appears both on the left side and right side of the equation. You can combine them since they are similar.