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Beliebt Rechnen >

derivative f(x)=5x^2-x^{1/3}

Lösung

ableitung von

f (x) = 5 x^{2} - x^{\frac{1}{3}}

Lösung

\frac{- 1 + 30 x ^{\frac{5}{3}}}{3 x ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (5 x^{2} - x^{\frac{1}{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (5 x^{2}) - \frac{d}{d x} (x^{\frac{1}{3}})

\frac{d}{d x} (5 x^{2}) = 10 x

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

= 10 x - \frac{1}{3 x ^{\frac{2}{3}}}

Vereinfache

10 x - \frac{1}{3 x ^{\frac{2}{3}}} : \frac{- 1 + 30 x ^{\frac{5}{3}}}{3 x ^{\frac{2}{3}}}

= \frac{- 1 + 30 x ^{\frac{5}{3}}}{3 x ^{\frac{2}{3}}}

Graph

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