Polynomials- Prove that function can be only polynomial – math.stackexchange.com

Polynomials- Prove that function can be only polynomial – math.stackexchange.com

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Suppose there exist a function $f : \mathbb R \to \mathbb R$ such that $f(x)\cdot f'(x)$ is polynomial It. is trivial that if $f(x)$ is polynomial, then $f(x)\cdot f'(x)$ is polynomial. My question ...

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