derivative 3x^{1/3}-5x^{4/3}

Lösung

ableitung von

3 x^{\frac{1}{3}} - 5 x^{\frac{4}{3}}

\frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (3 x^{\frac{1}{3}} - 5 x^{\frac{4}{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 x^{\frac{1}{3}}) - \frac{d}{d x} (5 x^{\frac{4}{3}})

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

\frac{d}{d x} (5 x^{\frac{4}{3}}) = \frac{20 x ^{\frac{1}{3}}}{3}

= \frac{1}{x ^{\frac{2}{3}}} - \frac{20 x ^{\frac{1}{3}}}{3}

Vereinfache

\frac{1}{x ^{\frac{2}{3}}} - \frac{20 x ^{\frac{1}{3}}}{3} : \frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

= \frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

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