(x/((x+1)^2))^'

Lösung

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

\frac{1 - x}{( x + 1 ) ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

x^{'} = 1

((x + 1)^{2})^{'} = 2 (x + 1)

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

Vereinfache

\frac{1 \cdot ( x + 1 ) ^{2} - 2 ( x + 1 ) x}{( ( x + 1 ) ^{2} ) ^{2}} : \frac{1 - x}{( x + 1 ) ^{3}}

= \frac{1 - x}{( x + 1 ) ^{3}}

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