Calculus: Early Transcendentals (2nd Edition)

For the given function $f$ the symbol $f'$ represents the derivative function of the function $f$.
For the given function $f$ the symbol $f'$ represents the derivative function of the function $f$. This is the mapping, similarly as $f$ in contrast to $f(x)$ and $f'(x)$ which are the values of those functions at $x$.