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Let \(f\) be the function defined on \((0, +\infty)\) by:$$ f(x) = 2\ln(x) - \dfrac{4}{x} $$
  1. Show that for all \(x \in (0, +\infty)\), \(f'(x) = \dfrac{2x+4}{x^2}\).
  2. Deduce that \(f\) is strictly increasing on \((0, +\infty)\).

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