derivative y=(((x^2+8))/(x^2-8))

Lösung

ableitung von

y = (\frac{( x ^{2} + 8 )}{x ^{2} - 8})

- \frac{32 x}{( x ^{2} - 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 8}{x ^{2} - 8})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} + 8 ) ( x ^{2} - 8 ) - \frac{d}{d x} ( x ^{2} - 8 ) ( x ^{2} + 8 )}{( x ^{2} - 8 ) ^{2}}

\frac{d}{d x} (x^{2} + 8) = 2 x

\frac{d}{d x} (x^{2} - 8) = 2 x

= \frac{2 x ( x ^{2} - 8 ) - 2 x ( x ^{2} + 8 )}{( x ^{2} - 8 ) ^{2}}

Vereinfache

\frac{2 x ( x ^{2} - 8 ) - 2 x ( x ^{2} + 8 )}{( x ^{2} - 8 ) ^{2}} : - \frac{32 x}{( x ^{2} - 8 ) ^{2}}

= - \frac{32 x}{( x ^{2} - 8 ) ^{2}}

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