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Beliebt Rechnen >

derivative 1/x+1/(x^2)+1/(x^3)

Lösung

ableitung von

\frac{1}{x} + \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

Lösung

- \frac{1}{x ^{2}} - \frac{2}{x ^{3}} - \frac{3}{x ^{4}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

= - \frac{1}{x ^{2}} - \frac{2}{x ^{3}} - \frac{3}{x ^{4}}

Graph

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