The function satisfies $f\left(x^2\right)f^{\text{'}\text{'}}\left(x\right)=f^{\text{'}}\left(x\right)f^{\text{'}}\left(x^2\right)$ for all real $x$. Given that $f\left(1\right)=1$ and $f^{\text{'}\text{'}\text{'}}\left(1\right)=8,$ then the value of $f^{\text{'}}\left(1\right)+f^{\text{'}\text{'}}\left(1\right)$ is equal to