Derivative of an extreme function composition

$f(x)$ is a polynomial function, where $f(0)=0$ and $f'(0)=2$ .

The derivative of $f^{2018}(x)$ with respect to $x$ at $x=0$ can be written as $a^b$ , where $a$ and $b$ are positive integers and $a$ is as small as possible. Find $a+b$ .

Note: superscript denotes composition, for example $f^{2}(x)=f(f(x))$