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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...

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