derivative (((x+11))/((x-11)))^5

Lösung

ableitung von

(\frac{( x + 11 )}{( x - 11 )})^{5}

- \frac{110 ( x + 11 ) ^{4}}{( x - 11 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x + 11}{x - 11})^{5})

Wende die Kettenregel an:

5 (\frac{x + 11}{x - 11})^{4} \frac{d}{d x} (\frac{x + 11}{x - 11})

= 5 (\frac{x + 11}{x - 11})^{4} \frac{d}{d x} (\frac{x + 11}{x - 11})

\frac{d}{d x} (\frac{x + 11}{x - 11}) = - \frac{22}{( x - 11 ) ^{2}}

= 5 (\frac{x + 11}{x - 11})^{4} (- \frac{22}{( x - 11 ) ^{2}})

Vereinfache

5 (\frac{x + 11}{x - 11})^{4} (- \frac{22}{( x - 11 ) ^{2}}) : - \frac{110 ( x + 11 ) ^{4}}{( x - 11 ) ^{6}}

= - \frac{110 ( x + 11 ) ^{4}}{( x - 11 ) ^{6}}

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