derivative of ((2x/(x^2+1))^2)

Lösung

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

\frac{8 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 \cdot \frac{2 x}{x ^{2} + 1} \cdot \frac{2 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}} : \frac{8 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

= \frac{8 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

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