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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{10 ( 2 x - 3 )}{( x ^{2} - 3 x ) ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

5 (- \frac{2}{( x ^{2} - 3 x ) ^{3}} (2 x - 3)) : - \frac{10 ( 2 x - 3 )}{( x ^{2} - 3 x ) ^{3}}

= - \frac{10 ( 2 x - 3 )}{( x ^{2} - 3 x ) ^{3}}

Graph

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