The answer you got is almost right. It should be:

I'm going to name this equation as follows

I'm using f instead of the traditional y so the equation makes sense

The chain rule states

In your case where

Then when:

So using the chain rule in this case you get:

Substituting y back in it becomes:

You had the right idea and almost got it correct. The chain rule can be easy to mess up especially when y is involved.