Will you integrate it 2015 times? - XII

Calculus Level 3

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? .
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