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Beliebt Rechnen >

derivative f(x)=\sqrt[5]{x}

Lösung

ableitung von

f (x) = 5 x

Lösung

\frac{1}{5 x ^{\frac{4}{5}}}

Schritte zur Lösung

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

Wende Radikal Regel an:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

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

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

Graph

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\int_{- 2}^{3} \frac{47}{x ^{4}} d x

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