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Beliebt Rechnen >

derivative of 4/5 x^{5/4}

Lösung

\frac{d}{d x} (\frac{4}{5} x^{\frac{5}{4}})

Lösung

x^{\frac{1}{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4}{5} x^{\frac{5}{4}})

Entferne die Konstante:

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

= \frac{4}{5} \frac{d}{d x} (x^{\frac{5}{4}})

Wende die Potenzregel an:

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

= \frac{4}{5} \cdot \frac{5}{4} x^{\frac{5}{4} - 1}

Vereinfache

\frac{4}{5} \cdot \frac{5}{4} x^{\frac{5}{4} - 1} : x^{\frac{1}{4}}

= x^{\frac{1}{4}}

Graph

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