Answer
$f'(a)=\lim \limits_{h \to 0}(3a^2+3ah+h^2+2)$, which equals to $3a^2+2$.
$f'(2)=3\times 2^2+2=14$
Work Step by Step
The algebraic derivative of a function can be described as:
$f'(a)=\lim \limits_{h \to 0}\frac{f(a+h)-f(a)}{h}$
Here, $f(a)=a^3+2a$
By substituting, we get:
$\frac{(a+h)^3+2(a+h)-(a^3+2a)}{h}=\frac{a^3+3a^2h+3ah^2+h^3+2a+2h-a^3-2a}{h}=\frac{3a^2h+3ah^2+h^3+2h}{h}=3a^2+3ah+h^2+2$
$f'(a)=\lim \limits_{h \to 0}(3a^2+3ah+h^2+2)$, which equals to $3a^2+2$.
$f'(2)=3\times 2^2+2=14$
