Answer
$7$
Work Step by Step
To take the derivative of a function using the limit process, plug into the equation $f'(x)=\lim\limits_{h \to 0}\frac{f(x+h)-f(x)}{h}$ and simplify:
$f'(x)=\lim\limits_{h \to 0}\frac{(7(x+h)-3)-(7x-3)}{h}$
$f'(x)=\lim\limits_{h \to 0}\frac{7x+7h-3-7x+3}{h}$
$f'(x)=\lim\limits_{h \to 0}\frac{7h}{h}$
$f'(x)=7$
(the $x$- and $h$-values will cancel each other out in many situations)
