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Beliebt Rechnen >

derivative of 1/(2x-5)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{1}{( 2 x - 5 ) ^{2}} \cdot 2 : - \frac{2}{( 2 x - 5 ) ^{2}}

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

Graph

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