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
Answer & explanation
Correct answer: option 2
We have
$f\left(x^3\right)=x^5$ for all $x \in R, x \neq 0$
Differentiating w.r.t. x, we get
$3 x^2 f'\left(x^3\right)=5 x^4 \Rightarrow f'\left(x^3\right)=\frac{5}{3} x^2 \Rightarrow f'(8)=\frac{20}{3}$