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Beliebt Rechnen >

derivative of-9/((6x+3^{3/2)})

Lösung

\frac{d}{d x} (- \frac{9}{( 6 x + 3 ) ^{\frac{3}{2}}})

Lösung

\frac{81}{( 6 x + 3 ) ^{\frac{5}{2}}}

Schritte zur Lösung

\frac{d}{d x} (- \frac{9}{( 6 x + 3 ) ^{\frac{3}{2}}})

Entferne die Konstante:

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

= - 9 \frac{d}{d x} (\frac{1}{( 6 x + 3 ) ^{\frac{3}{2}}})

Wende Exponentenregel an:

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

= - 9 \frac{d}{d x} ((6 x + 3)^{- \frac{3}{2}})

Wende die Kettenregel an:

- \frac{3}{2 ( 6 x + 3 ) ^{\frac{5}{2}}} \frac{d}{d x} (6 x + 3)

= - \frac{3}{2 ( 6 x + 3 ) ^{\frac{5}{2}}} \frac{d}{d x} (6 x + 3)

\frac{d}{d x} (6 x + 3) = 6

= - 9 (- \frac{3}{2 ( 6 x + 3 ) ^{\frac{5}{2}}} \cdot 6)

Vereinfache

- 9 (- \frac{3}{2 ( 6 x + 3 ) ^{\frac{5}{2}}} \cdot 6) : \frac{81}{( 6 x + 3 ) ^{\frac{5}{2}}}

= \frac{81}{( 6 x + 3 ) ^{\frac{5}{2}}}

Graph

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