a) Is there a one-to one and onto function $f: (0,1)\longrightarrow (0,1)$ such that $f'=f^{-1}$, i.e. the derivative of $f$ equals the inverse of $f$?

b) Is there a one-to one and onto function $f: (0,\infty)\longrightarrow (0,\infty)$ such that $f'=f^{-1}$, i.e. the derivative of $f$ equals the inverse of $f$?