derivative of 1/(8x-1)

Lösung

\frac{d}{d x} (\frac{1}{8 x - 1})

- \frac{8}{( 8 x - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{8 x - 1})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((8 x - 1)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 8 x - 1 ) ^{2}} \frac{d}{d x} (8 x - 1)

= - \frac{1}{( 8 x - 1 ) ^{2}} \frac{d}{d x} (8 x - 1)

\frac{d}{d x} (8 x - 1) = 8

= - \frac{1}{( 8 x - 1 ) ^{2}} \cdot 8

Vereinfache

- \frac{1}{( 8 x - 1 ) ^{2}} \cdot 8 : - \frac{8}{( 8 x - 1 ) ^{2}}

= - \frac{8}{( 8 x - 1 ) ^{2}}

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