derivative y=((x^2+6)/(x^2-6))^3

Lösung

ableitung von

y = (\frac{x ^{2} + 6}{x ^{2} - 6})^{3}

- \frac{72 x ( x ^{2} + 6 ) ^{2}}{( x ^{2} - 6 ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x ^{2} + 6}{x ^{2} - 6})^{3})

Wende die Kettenregel an:

3 (\frac{x ^{2} + 6}{x ^{2} - 6})^{2} \frac{d}{d x} (\frac{x ^{2} + 6}{x ^{2} - 6})

= 3 (\frac{x ^{2} + 6}{x ^{2} - 6})^{2} \frac{d}{d x} (\frac{x ^{2} + 6}{x ^{2} - 6})

\frac{d}{d x} (\frac{x ^{2} + 6}{x ^{2} - 6}) = - \frac{24 x}{( x ^{2} - 6 ) ^{2}}

= 3 (\frac{x ^{2} + 6}{x ^{2} - 6})^{2} (- \frac{24 x}{( x ^{2} - 6 ) ^{2}})

Vereinfache

3 (\frac{x ^{2} + 6}{x ^{2} - 6})^{2} (- \frac{24 x}{( x ^{2} - 6 ) ^{2}}) : - \frac{72 x ( x ^{2} + 6 ) ^{2}}{( x ^{2} - 6 ) ^{4}}

= - \frac{72 x ( x ^{2} + 6 ) ^{2}}{( x ^{2} - 6 ) ^{4}}

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