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Beliebt Rechnen >

derivative of (-5/(2x^6-4x^3-6x))

Lösung

\frac{d}{d x} (\frac{- 5}{2 x ^{6} - 4 x ^{3} - 6 x})

Lösung

\frac{15 ( 2 x ^{5} - 2 x ^{2} - 1 )}{2 x ^{2} ( x ^{5} - 2 x ^{2} - 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{- 5}{2 x ^{6} - 4 x ^{3} - 6 x})

Vereinfache

\frac{- 5}{2 x ^{6} - 4 x ^{3} - 6 x} : - \frac{5}{2 x ^{6} - 4 x ^{3} - 6 x}

= \frac{d}{d x} (- \frac{5}{2 x ^{6} - 4 x ^{3} - 6 x})

Entferne die Konstante:

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

= - 5 \frac{d}{d x} (\frac{1}{2 x ^{6} - 4 x ^{3} - 6 x})

Wende Exponentenregel an:

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

= - 5 \frac{d}{d x} ((2 x^{6} - 4 x^{3} - 6 x)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 2 x ^{6} - 4 x ^{3} - 6 x ) ^{2}} \frac{d}{d x} (2 x^{6} - 4 x^{3} - 6 x)

= - \frac{1}{( 2 x ^{6} - 4 x ^{3} - 6 x ) ^{2}} \frac{d}{d x} (2 x^{6} - 4 x^{3} - 6 x)

\frac{d}{d x} (2 x^{6} - 4 x^{3} - 6 x) = 12 x^{5} - 12 x^{2} - 6

= - 5 (- \frac{1}{( 2 x ^{6} - 4 x ^{3} - 6 x ) ^{2}} (12 x^{5} - 12 x^{2} - 6))

Vereinfache

- 5 (- \frac{1}{( 2 x ^{6} - 4 x ^{3} - 6 x ) ^{2}} (12 x^{5} - 12 x^{2} - 6)) : \frac{15 ( 2 x ^{5} - 2 x ^{2} - 1 )}{2 x ^{2} ( x ^{5} - 2 x ^{2} - 3 ) ^{2}}

= \frac{15 ( 2 x ^{5} - 2 x ^{2} - 1 )}{2 x ^{2} ( x ^{5} - 2 x ^{2} - 3 ) ^{2}}

Graph

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steigung sin(2θ)

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