Derivata 1^ e 2^

Question

[attach]118955[/attach] Spiegare gentilmente i ragionamenti, i passaggi e argomentare.

cmc · Accepted Answer

$ y(x) = arcsin( frac {x-1}{x+1}) -2 arccos( frac {x-1}{x+1}) $ D(y(x)) = frac {1}{ sqrt {1-( frac {(x-1)^2}{x+1)^2}}}D( frac {x-1}{x+1}) +2 frac {1}{ sqrt {1-( frac {(x-1)^2}{x+1)^2}}}D( frac {x-1}{x+1}) $             $=3 frac {1}{ sqrt {1-( frac {(x-1)^2}{x+1)^2}}}D( frac {x-1}{x+1}) $            $=3 frac {1}{ sqrt {1-( frac {(x-1)^2}{x+1)^2}}} frac {2}{(x+1)^2} $            $=3 frac {x+1}{ sqrt {(x+1)^2-(x-1)^2}}  frac {2}{(x+1)^2} $             $=3 frac {1}{ sqrt {4x}}  frac {2}{x+1} $            $= frac {3}{2 sqrt {x}}  frac {2}{x+1} $             $= frac {3}{(x+1) sqrt {x}} $

Derivata 1^ e 2^

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