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Beliebt Rechnen >

derivative of-1/3 (x^{-3}-x^6)

Lösung

\frac{d}{d x} (- \frac{1}{3} (x^{- 3} - x^{6}))

Lösung

\frac{2 x ^{9} + 1}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (- \frac{1}{3} (x^{- 3} - x^{6}))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{3} \frac{d}{d x} (x^{- 3} - x^{6})

Wende die Summen-/Differenzregel an:

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

= - \frac{1}{3} (\frac{d}{d x} (x^{- 3}) - \frac{d}{d x} (x^{6}))

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

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

= - \frac{1}{3} (- \frac{3}{x ^{4}} - 6 x^{5})

Vereinfache

- \frac{1}{3} (- \frac{3}{x ^{4}} - 6 x^{5}) : \frac{2 x ^{9} + 1}{x ^{4}}

= \frac{2 x ^{9} + 1}{x ^{4}}

Graph

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