derivative ((5x-1)/(4x+2))^{-5}

Lösung

ableitung von

(\frac{5 x - 1}{4 x + 2})^{- 5}

- \frac{1120 ( 2 x + 1 ) ^{4}}{( 5 x - 1 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{5 x - 1}{4 x + 2})^{- 5})

Wende die Kettenregel an:

- \frac{5}{( \frac{5 x - 1}{4 x + 2} ) ^{6}} \frac{d}{d x} (\frac{5 x - 1}{4 x + 2})

= - \frac{5}{( \frac{5 x - 1}{4 x + 2} ) ^{6}} \frac{d}{d x} (\frac{5 x - 1}{4 x + 2})

\frac{d}{d x} (\frac{5 x - 1}{4 x + 2}) = \frac{7}{2 ( 2 x + 1 ) ^{2}}

= - \frac{5}{( \frac{5 x - 1}{4 x + 2} ) ^{6}} \cdot \frac{7}{2 ( 2 x + 1 ) ^{2}}

Vereinfache

- \frac{5}{( \frac{5 x - 1}{4 x + 2} ) ^{6}} \cdot \frac{7}{2 ( 2 x + 1 ) ^{2}} : - \frac{1120 ( 2 x + 1 ) ^{4}}{( 5 x - 1 ) ^{6}}

= - \frac{1120 ( 2 x + 1 ) ^{4}}{( 5 x - 1 ) ^{6}}

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