derivative of 1/(4x-7)

Lösung

\frac{d}{d x} (\frac{1}{4 x - 7})

- \frac{4}{( 4 x - 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{4 x - 7})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((4 x - 7)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 4 x - 7 ) ^{2}} \frac{d}{d x} (4 x - 7)

= - \frac{1}{( 4 x - 7 ) ^{2}} \frac{d}{d x} (4 x - 7)

\frac{d}{d x} (4 x - 7) = 4

= - \frac{1}{( 4 x - 7 ) ^{2}} \cdot 4

Vereinfache

- \frac{1}{( 4 x - 7 ) ^{2}} \cdot 4 : - \frac{4}{( 4 x - 7 ) ^{2}}

= - \frac{4}{( 4 x - 7 ) ^{2}}

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