Answer
$f'(2)=18$
Work Step by Step
$f(x)=x^3+6x$
$f'(c)=\lim\limits_{x \to c}\frac{f(x)-f(c)}{x-c}$
$f'(2)=\lim\limits_{x \to 2}\frac{x^3+6x-((2)^3+6(2))}{x-2}$
$f'(2)=\lim\limits_{x \to 2}\frac{x^3+6x-20}{x-2}$
$f'(2)=\lim\limits_{x \to 2}\frac{(x-2)(x^2+2x+10)}{x-2}$
$f'(2)=\lim\limits_{x \to 2}(x^2+2x+10)$
$f'(2)=18$
