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

**Edit:** ${f}^{-1}$ is the inverse compositional of $f$, for example $\log$ is the inverse application of exp function .

**Note 02**:  I have edited my question to clarify the titled question that related to ${f}^{-1}$


Thank you for any help