(9) (12 %) $A$ is an $n \times n$ symmetric real matrix and $f(x) = \langle Ax, x \rangle$, $x \in \mathbb{R}^n$, where $\langle x, y \rangle = \sum{i=1}^n xi yi$ for $x = (x1, \ldots, xn)$ and $y = (y1, \ldots, y_n)$ in $\mathbb{R}^n$. Show that $f$ is differentiable and find $Df(x)y$ for $x, y \in \mathbb{R}^n$.