derivative of \sqrt[3]{x}-4/x

Lösung

\frac{d}{d x} (3 x - \frac{4}{x})

\frac{x ^{2} + 12 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

Schritte zur Lösung

\frac{d}{d x} (3 x - \frac{4}{x})

Wende die Summen-/Differenzregel an:

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

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

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

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

= \frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{4}{x ^{2}})

Vereinfache

\frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{4}{x ^{2}}) : \frac{x ^{2} + 12 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

= \frac{x ^{2} + 12 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

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