derivative of \sqrt[5]{x}-8/x

Lösung

\frac{d}{d x} (5 x - \frac{8}{x})

\frac{x ^{2} + 40 x ^{\frac{4}{5}}}{5 x ^{\frac{14}{5}}}

Schritte zur Lösung

\frac{d}{d x} (5 x - \frac{8}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (5 x) - \frac{d}{d x} (\frac{8}{x})

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

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

= \frac{1}{5 x ^{\frac{4}{5}}} - (- \frac{8}{x ^{2}})

Vereinfache

\frac{1}{5 x ^{\frac{4}{5}}} - (- \frac{8}{x ^{2}}) : \frac{x ^{2} + 40 x ^{\frac{4}{5}}}{5 x ^{\frac{14}{5}}}

= \frac{x ^{2} + 40 x ^{\frac{4}{5}}}{5 x ^{\frac{14}{5}}}

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