Let $f$ be a function such that :$f:\mathbb{R}\to \mathbb{R}$ and $f^{-1}$ is a reciprocal function of $f$ I w'd like to know how do i solve this class of differencial equation : $$\displaystyle \ f'= e^{\displaystyle {f}^{-1}}$$ ?.

Note: $f' =\displaystyle\frac{df}{dx}$.

Thank you for any help