((x^2)/(2x+4))^'

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

(2 x + 4)^{'} = 2

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

Vereinfache

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

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

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