derivative of 1/(x^6+1/(x^7))

Lösung

\frac{d}{d x} (\frac{1}{x ^{6}} + \frac{1}{x ^{7}})

- \frac{6}{x ^{7}} - \frac{7}{x ^{8}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{6}} + \frac{1}{x ^{7}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{1}{x ^{6}}) + \frac{d}{d x} (\frac{1}{x ^{7}})

\frac{d}{d x} (\frac{1}{x ^{6}}) = - \frac{6}{x ^{7}}

\frac{d}{d x} (\frac{1}{x ^{7}}) = - \frac{7}{x ^{8}}

= - \frac{6}{x ^{7}} - \frac{7}{x ^{8}}

d er i v a t i v e (x^{2} + 8) (5 - x)

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