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Beliebt Rechnen >

derivative of-1/(x^2-7/x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

Graph

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