Will you integrate it 2015 times? - XII

A function $f : \mathbb{R} \rightarrow \mathbb{R}$ is at least $2015$ times differentiable. $f(x)$ is differentiated $2015$ times to get $g(x) = \dfrac{ d^{2015} }{dx^{2015} } \big[ f(x) \big]$ .

If $f(x)$ is a periodic function with a fundamental period $p$ , then what can be said about $g(x)$ ?
Choose the most appropriate option.

This problem is part of the set - Will you integrate it 2015 times? .