Let $f$ be a differentiable function of $x$ (whose formula is not known) and recall that $\frac{d}{dx}[f(x)]$ and $f'(x)$ are interchangeable notations. Using the $f'$ notation, determine the following derivative in terms of $x$ and the unknown function $f$.

$\frac{d}{dx}[x^{2}f\!\left(x\right)] =$