derivative 1/(sqrt(x^9))

Lösung

ableitung von

\frac{1}{x ^{9}}

- \frac{9 x ^{8}}{2 ( x ^{9} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{9}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{9}) = 9 x^{8}

= - \frac{1}{2 ( x ^{9} ) ^{\frac{3}{2}}} \cdot 9 x^{8}

Vereinfache

- \frac{1}{2 ( x ^{9} ) ^{\frac{3}{2}}} \cdot 9 x^{8} : - \frac{9 x ^{8}}{2 ( x ^{9} ) ^{\frac{3}{2}}}

= - \frac{9 x ^{8}}{2 ( x ^{9} ) ^{\frac{3}{2}}}

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