derivative f(x)= 1/(sqrt(x^{17))}

Lösung

ableitung von

f (x) = \frac{1}{x ^{17}}

- \frac{17 x ^{16}}{2 ( x ^{17} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{17}})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x^{17})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( x ^{17} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{17})

= - \frac{1}{2 ( x ^{17} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{17})

\frac{d}{d x} (x^{17}) = 17 x^{16}

= - \frac{1}{2 ( x ^{17} ) ^{\frac{3}{2}}} \cdot 17 x^{16}

Vereinfache

- \frac{1}{2 ( x ^{17} ) ^{\frac{3}{2}}} \cdot 17 x^{16} : - \frac{17 x ^{16}}{2 ( x ^{17} ) ^{\frac{3}{2}}}

= - \frac{17 x ^{16}}{2 ( x ^{17} ) ^{\frac{3}{2}}}

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