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Beliebt Rechnen >

(x/(1+x^2))^'

Lösung

(\frac{x}{1 + x ^{2}})^{^{'}}

Lösung

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

Schritte zur Lösung

(\frac{x}{1 + x ^{2}})^{'}

Wende die Quotientenregel an:

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

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

x^{'} = 1

(1 + x^{2})^{'} = 2 x

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

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

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

Graph

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