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Beliebt Rechnen >

derivative ln(\sqrt[5]{x})

Lösung

ableitung von

ln (5 x)

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (5 x) = \frac{1}{5 x ^{\frac{4}{5}}}

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

Vereinfache

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

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

Graph

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