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Beliebt Rechnen >

derivative of-(15/(16x^{7/2)})

Lösung

\frac{d}{d x} (- \frac{15}{16 x ^{\frac{7}{2}}})

Lösung

\frac{105}{32 x ^{\frac{9}{2}}}

Schritte zur Lösung

\frac{d}{d x} (- \frac{15}{16 x ^{\frac{7}{2}}})

Entferne die Konstante:

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

= - \frac{15}{16} \frac{d}{d x} (\frac{1}{x ^{\frac{7}{2}}})

Wende Exponentenregel an:

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

= - \frac{15}{16} \frac{d}{d x} (x^{- \frac{7}{2}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - \frac{15}{16} (- \frac{7}{2} x^{- \frac{7}{2} - 1})

Vereinfache

- \frac{15}{16} (- \frac{7}{2} x^{- \frac{7}{2} - 1}) : \frac{105}{32 x ^{\frac{9}{2}}}

= \frac{105}{32 x ^{\frac{9}{2}}}

Graph

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