\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f : \mathbb{R} \to \mathbb{R}\), \(f(x) = x^5 + x\). Show that \(f\) is a \(C^\infty\) bijection, then apply the inverse-map derivative formula to compute \((f^{-1})'(2)\).
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