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Beliebt Rechnen >

derivative of ln(x^{1/3})

Lösung

\frac{d}{d x} (ln (x^{\frac{1}{3}}))

Lösung

\frac{1}{3 x}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{\frac{1}{3}}))

Wende die Kettenregel an:

\frac{1}{x ^{\frac{1}{3}}} \frac{d}{d x} (x^{\frac{1}{3}})

= \frac{1}{x ^{\frac{1}{3}}} \frac{d}{d x} (x^{\frac{1}{3}})

\frac{d}{d x} (x^{\frac{1}{3}}) = \frac{1}{3 x ^{\frac{2}{3}}}

= \frac{1}{x ^{\frac{1}{3}}} \cdot \frac{1}{3 x ^{\frac{2}{3}}}

Vereinfache

\frac{1}{x ^{\frac{1}{3}}} \cdot \frac{1}{3 x ^{\frac{2}{3}}} : \frac{1}{3 x}

= \frac{1}{3 x}

Graph

Beliebte Beispiele

derivative of cos(x(1+sin(x)^{10}))

\frac{d}{d x} (cos (x (1 + sin (x))^{10}))

f(x)=2cos(x^3)-2/x

f (x) = 2 cos (x^{3}) - \frac{2}{x}

f(p)=sqrt(325-3p)

f (p) = 325 - 3 p

integral of sqrt(8x+4)

\int 8 x + 4 d x

\frac{d y}{y} = x d x