\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that \(f : \mathbb{R} \to \mathbb{R}\), \(f(x) = x^2\), is differentiable at every \(a \in \mathbb{R}\) and compute \(f'(a)\) from the difference quotient.
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