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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

ma c l a u r in ln (1 + 4 x)

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