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Beliebt Rechnen >

derivative ((x+9)/(x-9))^5

Lösung

ableitung von

(\frac{x + 9}{x - 9})^{5}

Lösung

- \frac{90 ( x + 9 ) ^{4}}{( x - 9 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x + 9}{x - 9})^{5})

Wende die Kettenregel an:

5 (\frac{x + 9}{x - 9})^{4} \frac{d}{d x} (\frac{x + 9}{x - 9})

= 5 (\frac{x + 9}{x - 9})^{4} \frac{d}{d x} (\frac{x + 9}{x - 9})

\frac{d}{d x} (\frac{x + 9}{x - 9}) = - \frac{18}{( x - 9 ) ^{2}}

= 5 (\frac{x + 9}{x - 9})^{4} (- \frac{18}{( x - 9 ) ^{2}})

Vereinfache

5 (\frac{x + 9}{x - 9})^{4} (- \frac{18}{( x - 9 ) ^{2}}) : - \frac{90 ( x + 9 ) ^{4}}{( x - 9 ) ^{6}}

= - \frac{90 ( x + 9 ) ^{4}}{( x - 9 ) ^{6}}

Graph

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