The first problem is your notation.

By ' I'm assuming you mean

So when you differentiate x wrt s you get one, but when you differentiate

y wrt x you get and not 1.

NOTE.... I inserted that y' just now in my copy of your solution to 1

UNLESS the prime means .

For

you can divide inside the () and get (1+...).

BUt it's better to learn how to do this by scratch.

Let , then take log's of both sides, that pulls down the exponent x.

Work on this and I'll check it later.

The point to this problem is to make it into a fraction and apply L'Hopitals' Rule.