Derivative of $f(x)\cdot x$ where $f$ is a $\mathbb{R}^3$ function: how to compute it?

Let $f:\mathbb{R}^3\to\mathbb{R}^3$. Could someone please help me to compute the the derivative of$$f(x)\cdot x?$$

If $f$ would be a real valued function I think it should be the derivative of a product, but how to proceed in this case?

Thank you in advance.