I know that
$f_x=e^{t(x)}$
(where the notation $f_x=\frac{df}{dx}$)
(EDIT: $f=f(x)$ and $t$ parameterizes $x$, so $x=x(t) \Leftrightarrow t=t(x)$)
and that therefore
$\frac{d^n f_x}{dx^n}=\frac{e^t}{\dot{x}^n}$
(where $\dot{x}=\frac{dx}{dt}$)
I need to find out what the function $f(x)$ is from this information. Help appreciated.