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Let \(f\) be the function defined on \(\mathbb{R}\) by \(f(x) = \dfrac{1}{1+e^x}\).
  1. Show that for all \(x \in \mathbb{R}\), \(f'(x) = -\dfrac{e^x}{(1+e^x)^2}\).
  2. Study the variations of \(f\) on \(\mathbb{R}\) and dress its variation table.

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