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Beliebt Rechnen >

derivative of x^{2/3}-x^{1/3}+4

Lösung

\frac{d}{d x} (x^{\frac{2}{3}} - x^{\frac{1}{3}} + 4)

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{2}{3}} - x^{\frac{1}{3}} + 4)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{\frac{2}{3}}) - \frac{d}{d x} (x^{\frac{1}{3}}) + \frac{d}{d x} (4)

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

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

\frac{d}{d x} (4) = 0

= \frac{2}{3 x ^{\frac{1}{3}}} - \frac{1}{3 x ^{\frac{2}{3}}} + 0

Vereinfache

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

Graph

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