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 .
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.