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Beliebt Rechnen >

derivative of 5/(1-x)

Lösung

\frac{d}{d x} (\frac{5}{1 - x})

Lösung

\frac{5}{( 1 - x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{1 - x})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

= 5 \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

= 5 (- \frac{1}{( 1 - x ) ^{2}} (- 1))

Vereinfache

5 (- \frac{1}{( 1 - x ) ^{2}} (- 1)) : \frac{5}{( 1 - x ) ^{2}}

= \frac{5}{( 1 - x ) ^{2}}

Graph

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