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Beliebt Rechnen >

derivative of (-6/((1+x)^4))

Lösung

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

Lösung

\frac{24}{( 1 + x ) ^{5}}

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{4}{( 1 + x ) ^{5}} \frac{d}{d x} (1 + x)

= - \frac{4}{( 1 + x ) ^{5}} \frac{d}{d x} (1 + x)

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

= - 6 (- \frac{4}{( 1 + x ) ^{5}} \cdot 1)

Vereinfache

- 6 (- \frac{4}{( 1 + x ) ^{5}} \cdot 1) : \frac{24}{( 1 + x ) ^{5}}

= \frac{24}{( 1 + x ) ^{5}}

Graph

Beliebte Beispiele

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\int 2 x + 5 x^{- 2} d x

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integral of (7x^3-7)^4x^2

\int (7 x^{3} - 7)^{4} x^{2} d x