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Beliebt Rechnen >

derivative 3x^4-5x+2\sqrt[3]{x}

Lösung

ableitung von

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

Lösung

\frac{2 + 36 x ^{\frac{11}{3}}}{3 x ^{\frac{2}{3}}} - 5

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

\frac{d}{d x} (5 x) = 5

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

= 12 x^{3} - 5 + \frac{2}{3 x ^{\frac{2}{3}}}

Ziehe Brüche zusammen

\frac{2}{3 x ^{\frac{2}{3}}} + 12 x^{3} : \frac{2 + 36 x ^{\frac{11}{3}}}{3 x ^{\frac{2}{3}}}

= \frac{2 + 36 x ^{\frac{11}{3}}}{3 x ^{\frac{2}{3}}} - 5

Graph

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