derivative ((x^2+4)/(x^2-4))^2

Lösung

ableitung von

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

- \frac{32 x ( x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

= 2 \cdot \frac{x ^{2} + 4}{x ^{2} - 4} \frac{d}{d x} (\frac{x ^{2} + 4}{x ^{2} - 4})

\frac{d}{d x} (\frac{x ^{2} + 4}{x ^{2} - 4}) = - \frac{16 x}{( x ^{2} - 4 ) ^{2}}

= 2 \cdot \frac{x ^{2} + 4}{x ^{2} - 4} (- \frac{16 x}{( x ^{2} - 4 ) ^{2}})

Vereinfache

2 \cdot \frac{x ^{2} + 4}{x ^{2} - 4} (- \frac{16 x}{( x ^{2} - 4 ) ^{2}}) : - \frac{32 x ( x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}}

= - \frac{32 x ( x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}}

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