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Beliebt Rechnen >

derivative of ((x+1/(x-1))^4)

Lösung

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

Lösung

- \frac{8 ( x + 1 ) ^{3}}{( x - 1 ) ^{5}}

Schritte zur Lösung

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

Wende die Kettenregel an:

4 (\frac{x + 1}{x - 1})^{3} \frac{d}{d x} (\frac{x + 1}{x - 1})

= 4 (\frac{x + 1}{x - 1})^{3} \frac{d}{d x} (\frac{x + 1}{x - 1})

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

= 4 (\frac{x + 1}{x - 1})^{3} (- \frac{2}{( x - 1 ) ^{2}})

Vereinfache

4 (\frac{x + 1}{x - 1})^{3} (- \frac{2}{( x - 1 ) ^{2}}) : - \frac{8 ( x + 1 ) ^{3}}{( x - 1 ) ^{5}}

= - \frac{8 ( x + 1 ) ^{3}}{( x - 1 ) ^{5}}

Graph

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