1. We are given the function $$f(x,y) = x^2 - 3xy^2$$ and asked to find the partial derivative of $$f$$ with respect to $$y$$, denoted as $$\frac{\partial f}{\partial y}$$. 2. The partial derivative with respect to $$y$$ means we treat $$x$$ as a constant and differentiate only with respect to $$y$$. 3. The function is $$f(x,y) = x^2 - 3xy^2$$. 4. Differentiate each term with respect to $$y$$: - The derivative of $$x^2$$ with respect to $$y$$ is $$0$$ since $$x^2$$ is constant with respect to $$y$$. - The derivative of $$-3xy^2$$ with respect to $$y$$ is $$-3x \cdot 2y = -6xy$$ using the power rule and constant multiple rule. 5. Therefore, $$\frac{\partial f}{\partial y} = 0 - 6xy = -6xy$$. 6. The correct answer is $$-6xy$$.