derivative 8x^3+2x+7x^{1/3}

Lösung

ableitung von

8 x^{3} + 2 x + 7 x^{\frac{1}{3}}

\frac{7 + 72 x ^{\frac{8}{3}}}{3 x ^{\frac{2}{3}}} + 2

Schritte zur Lösung

\frac{d}{d x} (8 x^{3} + 2 x + 7 x^{\frac{1}{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (8 x^{3}) + \frac{d}{d x} (2 x) + \frac{d}{d x} (7 x^{\frac{1}{3}})

\frac{d}{d x} (8 x^{3}) = 24 x^{2}

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

\frac{d}{d x} (7 x^{\frac{1}{3}}) = \frac{7}{3 x ^{\frac{2}{3}}}

= 24 x^{2} + 2 + \frac{7}{3 x ^{\frac{2}{3}}}

Ziehe Brüche zusammen

\frac{7}{3 x ^{\frac{2}{3}}} + 24 x^{2} : \frac{7 + 72 x ^{\frac{8}{3}}}{3 x ^{\frac{2}{3}}}

= \frac{7 + 72 x ^{\frac{8}{3}}}{3 x ^{\frac{2}{3}}} + 2

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