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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{4}{( 1 + x ) ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- 2 (- \frac{2}{( 1 + x ) ^{3}} \cdot 1) : \frac{4}{( 1 + x ) ^{3}}

= \frac{4}{( 1 + x ) ^{3}}

Graph

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