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Beliebt Rechnen >

derivative of 2/(x^3+1)

Lösung

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

Lösung

- \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 (- \frac{1}{( x ^{3} + 1 ) ^{2}} \cdot 3 x^{2}) : - \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}}

= - \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}}

Graph

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