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Beliebt Rechnen >

derivative f(x)=-7sqrt(x)-2/(x^7)

Lösung

ableitung von

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

Lösung

\frac{7 ( - x ^{\frac{15}{2}} + 4 )}{2 x ^{\frac{15}{2}} x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (\frac{2}{x ^{7}}) = - \frac{14}{x ^{8}}

= - \frac{7}{2 x} - (- \frac{14}{x ^{8}})

Vereinfache

- \frac{7}{2 x} - (- \frac{14}{x ^{8}}) : \frac{7 ( - x ^{\frac{15}{2}} + 4 )}{2 x ^{\frac{15}{2}} x}

= \frac{7 ( - x ^{\frac{15}{2}} + 4 )}{2 x ^{\frac{15}{2}} x}

Graph

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