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Beliebt Rechnen >

derivative of 8/(1+x)

Lösung

\frac{d}{d x} (\frac{8}{1 + x})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{8}{1 + x})

Entferne die Konstante:

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

= 8 \frac{d}{d x} (\frac{1}{1 + x})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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