derivative f(x)=(2x^2+6x+6)/(x+1)

Lösung

ableitung von

f (x) = \frac{2 x ^{2} + 6 x + 6}{x + 1}

\frac{2 x ^{2} + 4 x}{( x + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{2} + 6 x + 6}{x + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x ^{2} + 6 x + 6 ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) ( 2 x ^{2} + 6 x + 6 )}{( x + 1 ) ^{2}}

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

\frac{d}{d x} (x + 1) = 1

= \frac{( 4 x + 6 ) ( x + 1 ) - 1 \cdot ( 2 x ^{2} + 6 x + 6 )}{( x + 1 ) ^{2}}

Vereinfache

\frac{( 4 x + 6 ) ( x + 1 ) - 1 \cdot ( 2 x ^{2} + 6 x + 6 )}{( x + 1 ) ^{2}} : \frac{2 x ^{2} + 4 x}{( x + 1 ) ^{2}}

= \frac{2 x ^{2} + 4 x}{( x + 1 ) ^{2}}

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