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Beliebt Rechnen >

derivative of (3000/(x+3600x^{-1)})

Lösung

\frac{d}{d x} (\frac{3000}{x + 3600 x ^{- 1}})

Lösung

- \frac{3000 ( x ^{2} - 3600 )}{( x ^{2} + 3600 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3000}{x + 3600 x ^{- 1}})

Entferne die Konstante:

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

= 3000 \frac{d}{d x} (\frac{1}{x + 3600 x ^{- 1}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 3000 \frac{d}{d x} ((x + 3600 x^{- 1})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x + 3600 x ^{- 1} ) ^{2}} \frac{d}{d x} (x + 3600 x^{- 1})

= - \frac{1}{( x + 3600 x ^{- 1} ) ^{2}} \frac{d}{d x} (x + 3600 x^{- 1})

\frac{d}{d x} (x + 3600 x^{- 1}) = 1 - \frac{3600}{x ^{2}}

= 3000 (- \frac{1}{( x + 3600 x ^{- 1} ) ^{2}} (1 - \frac{3600}{x ^{2}}))

Vereinfache

3000 (- \frac{1}{( x + 3600 x ^{- 1} ) ^{2}} (1 - \frac{3600}{x ^{2}})) : - \frac{3000 ( x ^{2} - 3600 )}{( x ^{2} + 3600 ) ^{2}}

= - \frac{3000 ( x ^{2} - 3600 )}{( x ^{2} + 3600 ) ^{2}}

Graph

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