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Beliebt Rechnen >

derivative of 2/(3x^{1/3})

Lösung

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

Lösung

- \frac{2}{9 x ^{\frac{4}{3}}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

\frac{2}{3} (- \frac{1}{3} x^{- \frac{1}{3} - 1}) : - \frac{2}{9 x ^{\frac{4}{3}}}

= - \frac{2}{9 x ^{\frac{4}{3}}}

Graph

Beliebte Beispiele

integral from 3 to 5 of x/(x^2-3)

\int_{3}^{5} \frac{x}{x ^{2} - 3} d x

derivative (6x^2-10x)e^x

d er i v a t i v e (6 x^{2} - 10 x) e^{x}

y^'=(y-xy)/(x^2)

y^{^{'}} = \frac{y - x y}{x ^{2}}

integral of 10sin^6(x)cos^3(x)

\int 10 sin^{6} (x) cos^{3} (x) d x

derivative e^{5sqrt(x)}

d er i v a t i v e e^{5 x}