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Beliebt Rechnen >

derivative f(x)=(2(-x^2+1))/((x^2+1))

Lösung

ableitung von

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

Lösung

- \frac{8 x}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

2 \cdot \frac{( - 2 x ) ( x ^{2} + 1 ) - 2 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}} : - \frac{8 x}{( x ^{2} + 1 ) ^{2}}

= - \frac{8 x}{( x ^{2} + 1 ) ^{2}}

Graph

Beliebte Beispiele

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