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Beliebt Rechnen >

derivative of 5/3 x^{2/3}

Lösung

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

Lösung

\frac{10}{9 x ^{\frac{1}{3}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

= \frac{5}{3} \cdot \frac{2}{3} x^{\frac{2}{3} - 1}

Vereinfache

\frac{5}{3} \cdot \frac{2}{3} x^{\frac{2}{3} - 1} : \frac{10}{9 x ^{\frac{1}{3}}}

= \frac{10}{9 x ^{\frac{1}{3}}}

Graph

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