I am solving a problem that is below
Let $n \in \mathbb{N}$ and let $f(x) = x^{1/n}$, $x \gt 0$. Prove that $f$ is differentiable on $(0,\infty)$ and find $f\,'$. (Hint: Note that $f = g^{−1}$, where $g(y) = y^n$, $y \gt 0$.)
My question is
1) I should use induction correct?
2) I am not sure how to get $f\,'$ via the hint. I know that $(f^{-1})'=1/f'(f^{-1})$ though I am not sure how to apply this...