Will you integrate it 2015 times? - V

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

True or False

If $\frac{f(x)}{g(x)}$ is constant for all values of $x$ , then $f(x)$ has to be of the form $Ae^{Bx}$ for some real numbers $A, B$ .

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