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Beliebt Rechnen >

derivative f(x)=(e^2)/(x^2-2x)

Lösung

ableitung von

f (x) = \frac{e ^{2}}{x ^{2} - 2 x}

Lösung

- \frac{e ^{2} ( 2 x - 2 )}{( x ^{2} - 2 x ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

= e^{2} (- \frac{1}{( x ^{2} - 2 x ) ^{2}} (2 x - 2))

Vereinfache

e^{2} (- \frac{1}{( x ^{2} - 2 x ) ^{2}} (2 x - 2)) : - \frac{e ^{2} ( 2 x - 2 )}{( x ^{2} - 2 x ) ^{2}}

= - \frac{e ^{2} ( 2 x - 2 )}{( x ^{2} - 2 x ) ^{2}}

Graph

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