derivative f(x)=-1/9 (x^{-9}-x^{18})

Lösung

ableitung von

f (x) = - \frac{1}{9} (x^{- 9} - x^{18})

\frac{2 x ^{27} + 1}{x ^{10}}

Schritte zur Lösung

\frac{d}{d x} (- \frac{1}{9} (x^{- 9} - x^{18}))

Entferne die Konstante:

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

= - \frac{1}{9} \frac{d}{d x} (x^{- 9} - x^{18})

Wende die Summen-/Differenzregel an:

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

= - \frac{1}{9} (\frac{d}{d x} (x^{- 9}) - \frac{d}{d x} (x^{18}))

\frac{d}{d x} (x^{- 9}) = - \frac{9}{x ^{10}}

\frac{d}{d x} (x^{18}) = 18 x^{17}

= - \frac{1}{9} (- \frac{9}{x ^{10}} - 18 x^{17})

Vereinfache

- \frac{1}{9} (- \frac{9}{x ^{10}} - 18 x^{17}) : \frac{2 x ^{27} + 1}{x ^{10}}

= \frac{2 x ^{27} + 1}{x ^{10}}

\int \frac{1}{16 e ^{- 5 x} + e ^{5 x}} d x

t an g e n t (4 - x) y^{2} = x^{3}, (2, 2)

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d er i v a t i v e f (x) = 0.0622 x^{2} + 1.1119 x + 2.3979