Problem of limit or limit of problem

You are given the curve $\sin(x) + \sin(y) = 1$ lying in the first quadrant. Given that for some constant $\alpha$ , the limit $\displaystyle \lim_{x\to0} x^\alpha \dfrac{d^2 y}{dx^2}$ exists and is non-zero. Find $2\alpha$ .

This problem is part of Math's Planet