derivative (x^2+5x+6)/(x^2-4)

Lösung

ableitung von

\frac{x ^{2} + 5 x + 6}{x ^{2} - 4}

- \frac{5}{( x - 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 5 x + 6}{x ^{2} - 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + 5 x + 6 ) ( x ^{2} - 4 ) - \frac{d}{d x} ( x ^{2} - 4 ) ( x ^{2} + 5 x + 6 )}{( x ^{2} - 4 ) ^{2}}

\frac{d}{d x} (x^{2} + 5 x + 6) = 2 x + 5

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

= \frac{( 2 x + 5 ) ( x ^{2} - 4 ) - 2 x ( x ^{2} + 5 x + 6 )}{( x ^{2} - 4 ) ^{2}}

Vereinfache

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

= - \frac{5}{( x - 2 ) ^{2}}

d er i v a t i v e \frac{2}{( 6 x ^{2} + 5 x + 1 ) ^{2}}

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