derivative of a polynomial function I'm struggling with the following task:
Let f: $\mathbb{R}^n \rightarrow \mathbb{R}$ be $$f(x_1,...,x_n)= \sum_{k,l=1}^n a_{kl}x_kx_l $$
when $a_{kl} \in \mathbb{R} \ \forall k,l \in $ {1,2,...,n} constant. Show that f is differentiable and calculate the derivative Df(x)  $ \forall x \in \mathbb{R}^n $.
Thanks for your help!

$Df(x) = \nabla f(x) = (\frac{\partial f}{\partial x_1}, \frac{\partial f}{\partial x_2},..., \frac{\partial f}{\partial x_n})$
$\frac{\partial f}{\partial x_i} = 2a_{ii}x_i + \Sigma_{k=1, k\ne i}^{n}a_{ki}x_k$
