The advantage of the derivative lies within not having to calculate the differential quotient over and over. Instead, you have a function in which you insert the point with the searched slope.
When differentiating the derivative, the derivative of the derivative function is called second derivative.
The derivative of the second derivative $f''$ is called third derivative etc.
$f'(x)$, $f''(x)$ und $f'''(x)$
After the third derivative, the style is usually the following:
The function $f(x)$ and its first two derivatives:
Calculating the derivative at point $x=1$: