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Beliebt Rechnen >

derivative of 1/(2sqrt(x+12))

Lösung

\frac{d}{d x} (\frac{1}{2 x + 12})

Lösung

- \frac{1}{4 ( x + 12 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2 x + 12})

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d x} (\frac{1}{x + 12})

Wende Exponentenregel an:

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

= \frac{1}{2} \frac{d}{d x} ((x + 12)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( x + 12 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 12)

= - \frac{1}{2 ( x + 12 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 12)

\frac{d}{d x} (x + 12) = 1

= \frac{1}{2} (- \frac{1}{2 ( x + 12 ) ^{\frac{3}{2}}} \cdot 1)

Vereinfache

\frac{1}{2} (- \frac{1}{2 ( x + 12 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{1}{4 ( x + 12 ) ^{\frac{3}{2}}}

= - \frac{1}{4 ( x + 12 ) ^{\frac{3}{2}}}

Graph

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