Show that if X has a density f such that f’ exists and is integrable?

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Show that if $X$ has a density $f$ such that $f'$ exists and is integrable, then its characteristic function has the property : $\phi(t)=ο(t^{-1} )$ as $t\to \infty$.

Hint: If $X$ has a density then its characteristic function has the property: $\lim_{t\to \infty}⁡\phi(t)=0$. You may use this result.

how can start with this hint to prove that any help