Let $f$ be a polynomial function such that $f\left(3x\right)=f^{\prime }\left(x\right). f^{\prime \prime }\left(x\right),$ for all $x\in R.$ Then :

Let $f:\mathit{R}\to \mathit{R}$ be defined as $f\left(x\right)=x^3+x-5$. If $g\left(x\right)$ is a function such that $f\left(g\left(x\right)\right)=x,\forall x\in \mathit{R}$, then $g^{\text{'}}\left(63\right)$ is equal to ______