derivative of 1/(sqrt(x^7))

Lösung

\frac{d}{d x} (\frac{1}{x ^{7}})

- \frac{7}{2 x ^{\frac{9}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{7}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{1}{2 ( x ^{7} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{7})

= - \frac{1}{2 ( x ^{7} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{7})

\frac{d}{d x} (x^{7}) = 7 x^{6}

= - \frac{1}{2 ( x ^{7} ) ^{\frac{3}{2}}} \cdot 7 x^{6}

Vereinfache

- \frac{1}{2 ( x ^{7} ) ^{\frac{3}{2}}} \cdot 7 x^{6} : - \frac{7}{2 x ^{\frac{9}{2}}}

= - \frac{7}{2 x ^{\frac{9}{2}}}

in v erse l a pl a ce \frac{4 s}{s ^{2} + 8 s + 20}

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