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Beliebt Rechnen >

derivative 8/((8-x^4)^{3/2)}

Lösung

ableitung von

\frac{8}{( 8 - x ^{4} ) ^{\frac{3}{2}}}

Lösung

\frac{48 x ^{3}}{( 8 - x ^{4} ) ^{\frac{5}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{8}{( 8 - x ^{4} ) ^{\frac{3}{2}}})

Entferne die Konstante:

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

= 8 \frac{d}{d x} (\frac{1}{( 8 - x ^{4} ) ^{\frac{3}{2}}})

Wende Exponentenregel an:

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

= 8 \frac{d}{d x} ((8 - x^{4})^{- \frac{3}{2}})

Wende die Kettenregel an:

- \frac{3}{2 ( 8 - x ^{4} ) ^{\frac{5}{2}}} \frac{d}{d x} (8 - x^{4})

= - \frac{3}{2 ( 8 - x ^{4} ) ^{\frac{5}{2}}} \frac{d}{d x} (8 - x^{4})

\frac{d}{d x} (8 - x^{4}) = - 4 x^{3}

= 8 (- \frac{3}{2 ( 8 - x ^{4} ) ^{\frac{5}{2}}} (- 4 x^{3}))

Vereinfache

8 (- \frac{3}{2 ( 8 - x ^{4} ) ^{\frac{5}{2}}} (- 4 x^{3})) : \frac{48 x ^{3}}{( 8 - x ^{4} ) ^{\frac{5}{2}}}

= \frac{48 x ^{3}}{( 8 - x ^{4} ) ^{\frac{5}{2}}}

Graph

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