Let f be a differentiable function defined for all $x \in R$ such that $f\left(x^3\right)=x^5$ for all $x \in R, x \neq 0$.Then, the value of f'(8), is

$\frac{20}{3}$

We have

$f\left(x^3\right)=x^5$  for all  $x \in R, x \neq 0$

Differentiating w.r.t. x, we get

$3 x^2 f'\left(x^3\right)=5 x^4 \Rightarrow f'\left(x^3\right)=\frac{5}{3} x^2 \Rightarrow f'(8)=\frac{20}{3}$