derivative of ln(x^{1/5})

Lösung

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

\frac{1}{5 x}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{1}{5 x}

\int x^{2} + x^{- 2} d x

sin (2 x) d x + cos (6 y) d y = 0

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\frac{\partial}{\partial x} (x e^{- x} (A x^{2} + B x + C))