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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

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x \to i lim (x - i)

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\frac{\partial}{\partial x} (e^{y^{2} - x^{2}})

(1+x^2)(dy)/(dx)-2xy=0

(1 + x^{2}) \frac{d y}{d x} - 2 x y = 0