derivative of-2/((x+1^3))

Lösung

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

\frac{6}{( x + 1 ) ^{4}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- 2 (- \frac{3}{( x + 1 ) ^{4}} \cdot 1) : \frac{6}{( x + 1 ) ^{4}}

= \frac{6}{( x + 1 ) ^{4}}

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