Use the definition of the derivative (don't be tempted to take shortcuts!) to find the derivative of the function $$f(x) = \frac{3 x + 6}{3 x + 8}.$$ Then, using interval notation, state the domain of the function and the domain of the derivative.

$f'(x)$ =

Domain of $f(x)$ =

Domain of $f'(x)$ =