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Beliebt Rechnen >

derivative of 1/(sqrt(3-x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

Graph

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