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Beliebt Rechnen >

derivative (x^2-1)/(x^2)

Lösung

ableitung von

\frac{x ^{2} - 1}{x ^{2}}

Lösung

\frac{2}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{2}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} - 1 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{2} - 1 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{2} - 1) = 2 x

\frac{d}{d x} (x^{2}) = 2 x

= \frac{2 x x ^{2} - 2 x ( x ^{2} - 1 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{2 x x ^{2} - 2 x ( x ^{2} - 1 )}{( x ^{2} ) ^{2}} : \frac{2}{x ^{3}}

= \frac{2}{x ^{3}}

Graph

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