$f(x) = \frac{1 + x \arctan x}{\sqrt{1 + x^2}}$

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Calcolare la derivata della funzione

$f(x) = frac{1 + x arctan x}{sqrt{1 + x^2}}$ $f'(x) = frac{( arctan x + frac{x}{1+x^2} ) cdot sqrt{1 + x^2} – (1 + x cdot arctan x) cdot frac{x}{sqrt{1 + x^2}}}{1 + x^2} =$ $frac{1}{1 + x^2} cdot g[ frac{arctan x cdot (1 + x^2) + x – x – x^2 arctan x}{sqrt{1 + x^2}} g] = frac{arctan x}{(1 + x^2)^{3/2}}$