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Beliebt Rechnen >

derivative of \sqrt[n]{x}

Lösung

\frac{d}{d x} (n x)

Lösung

\frac{x ^{\frac{1 - n}{n}}}{n}

Schritte zur Lösung

\frac{d}{d x} (n x)

Wende Radikal Regel an:

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

= \frac{d}{d x} (x^{\frac{1}{n}})

Wende die Potenzregel an:

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

= \frac{1}{n} x^{\frac{1}{n} - 1}

Vereinfache

\frac{1}{n} x^{\frac{1}{n} - 1} : \frac{x ^{\frac{1 - n}{n}}}{n}

= \frac{x ^{\frac{1 - n}{n}}}{n}

Graph

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