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Beliebt Rechnen >

derivative of 4/(sqrt(1-x))

Lösung

\frac{d}{d x} (\frac{4}{1 - x})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{4}{1 - x})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

= 4 \frac{d}{d x} ((1 - x)^{- \frac{1}{2}})

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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