derivative of (-2/(9x^{5/3)})

Lösung

\frac{d}{d x} (\frac{- 2}{9 x ^{\frac{5}{3}}})

\frac{10}{27 x ^{\frac{8}{3}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{- 2}{9 x ^{\frac{5}{3}}})

Vereinfache

\frac{- 2}{9 x ^{\frac{5}{3}}} : - \frac{2}{9 x ^{\frac{5}{3}}}

= \frac{d}{d x} (- \frac{2}{9 x ^{\frac{5}{3}}})

Entferne die Konstante:

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

= - \frac{2}{9} \frac{d}{d x} (\frac{1}{x ^{\frac{5}{3}}})

Wende Exponentenregel an:

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

= - \frac{2}{9} \frac{d}{d x} (x^{- \frac{5}{3}})

Wende die Potenzregel an:

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

= - \frac{2}{9} (- \frac{5}{3} x^{- \frac{5}{3} - 1})

Vereinfache

- \frac{2}{9} (- \frac{5}{3} x^{- \frac{5}{3} - 1}) : \frac{10}{27 x ^{\frac{8}{3}}}

= \frac{10}{27 x ^{\frac{8}{3}}}

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