The derivative of $x^2$ is $2x$, the derivative of $y^2$ is $2y \frac{dy}{dx}$ (since $y$ is a function of $x$), and the derivative of $\sin(xy^2)$ is $\cos(xy^2) \cdot (y^2 + 2xy\frac{dy}{dx})$ (using the chain rule and product rule). This gives us:
$$2x +
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