Will you integrate it 2015 times? - V

Calculus Level 3

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? .
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