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Beliebt Rechnen >

derivative f(x)=2x^2-6x^{1/3}

Lösung

ableitung von

f (x) = 2 x^{2} - 6 x^{\frac{1}{3}}

Lösung

\frac{- 2 + 4 x ^{\frac{5}{3}}}{x ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (2 x^{2} - 6 x^{\frac{1}{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 x^{2}) - \frac{d}{d x} (6 x^{\frac{1}{3}})

\frac{d}{d x} (2 x^{2}) = 4 x

\frac{d}{d x} (6 x^{\frac{1}{3}}) = \frac{2}{x ^{\frac{2}{3}}}

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

Vereinfache

4 x - \frac{2}{x ^{\frac{2}{3}}} : \frac{- 2 + 4 x ^{\frac{5}{3}}}{x ^{\frac{2}{3}}}

= \frac{- 2 + 4 x ^{\frac{5}{3}}}{x ^{\frac{2}{3}}}

Graph

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