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Beliebt Rechnen >

derivative of 1/(5x+2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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