Answer
$f'(x)=3$
Work Step by Step
$f(x)=3x-8$
Derivative of a function using the definition: $f'(x)=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h}$
To find $f(x+h)$, wherever you find $x$ in the function, substitute $x+h$
$f(x+h)=3(x+h)-8=3x+3h-8$
Let's plug in the components of the formula:
$f'(x)=\dfrac{3x+3h-8-3x+8}{h}=\dfrac{3h}{h}=3$
$f'(x)=3$
