1. The problem asks for the meaning of the notation $$\frac{\partial^2 f}{\partial y \partial x}$$ in terms of the order of partial differentiation. 2. This notation represents a second-order mixed partial derivative of the function $$f$$. 3. The order of differentiation is from right to left in the denominator: first with respect to $$x$$, then with respect to $$y$$. 4. Therefore, $$\frac{\partial^2 f}{\partial y \partial x} = \frac{\partial}{\partial y} \left( \frac{\partial f}{\partial x} \right)$$. 5. This means you first differentiate $$f$$ with respect to $$x$$, then differentiate the result with respect to $$y$$. 6. Let's analyze the options: - A. $$f_{yyx}$$ means differentiating twice with respect to $$y$$ and once with respect to $$x$$, which is not the same. - B. "First differentiate with respect to $$y$$, then with respect to $$x$$" is the reverse order. - C. "Differentiate with respect to both $$x$$ and $$y$$ simultaneously" is not how partial derivatives work. - D. "First differentiate with respect to $$x$$, then with respect to $$y$$" matches the notation. Final answer: Option D is correct.