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 $x$, the unknown function $f$, and the arbitrary constant $c$.

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