You use the chain rule when you have a function of a function: y = f(g(x)).
You use the product rule when you have a product of two functions: y = f(x) times g(x).
Sometimes both rules can be used.
can be thought of as a function of a function: , that is, the square of . On the other hand .....
can be thought of as a product of two functions: .
So in this case it doesn't matter whether you use the chain rule or the product rule.
However, what would your plan be to differentiate . Repeated use of the product rule? I hope NOT .....