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Beliebt Rechnen >

derivative y= 3/(x^6)+1/(x^5)-7/(x^2)

Lösung

ableitung von

y = \frac{3}{x ^{6}} + \frac{1}{x ^{5}} - \frac{7}{x ^{2}}

Lösung

- \frac{18}{x ^{7}} - \frac{5}{x ^{6}} + \frac{14}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{x ^{6}} + \frac{1}{x ^{5}} - \frac{7}{x ^{2}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{3}{x ^{6}}) + \frac{d}{d x} (\frac{1}{x ^{5}}) - \frac{d}{d x} (\frac{7}{x ^{2}})

\frac{d}{d x} (\frac{3}{x ^{6}}) = - \frac{18}{x ^{7}}

\frac{d}{d x} (\frac{1}{x ^{5}}) = - \frac{5}{x ^{6}}

\frac{d}{d x} (\frac{7}{x ^{2}}) = - \frac{14}{x ^{3}}

= - \frac{18}{x ^{7}} - \frac{5}{x ^{6}} - (- \frac{14}{x ^{3}})

Vereinfache

= - \frac{18}{x ^{7}} - \frac{5}{x ^{6}} + \frac{14}{x ^{3}}

Graph

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