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Beliebt Rechnen >

derivative (sqrt(x^5))/8

Lösung

ableitung von

\frac{x ^{5}}{8}

Lösung

\frac{5 x ^{\frac{3}{2}}}{16}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{5}}{8})

Entferne die Konstante:

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

= \frac{1}{8} \frac{d}{d x} (x^{5})

Wende Radikal Regel an:

n a^{m} = a^{\frac{m}{n}}

= \frac{1}{8} \frac{d}{d x} (x^{\frac{5}{2}})

Wende die Potenzregel an:

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

= \frac{1}{8} \cdot \frac{5}{2} x^{\frac{5}{2} - 1}

Vereinfache

\frac{1}{8} \cdot \frac{5}{2} x^{\frac{5}{2} - 1} : \frac{5 x ^{\frac{3}{2}}}{16}

= \frac{5 x ^{\frac{3}{2}}}{16}

Graph

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