d/(ds)((1-s^2)/((s^2+1)^2))

Lösung

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

- \frac{2 s ( - s ^{2} + 3 )}{( s ^{2} + 1 ) ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( - 2 s ) ( s ^{2} + 1 ) ^{2} - 4 s ( s ^{2} + 1 ) ( 1 - s ^{2} )}{( ( s ^{2} + 1 ) ^{2} ) ^{2}} : - \frac{2 s ( - s ^{2} + 3 )}{( s ^{2} + 1 ) ^{3}}

= - \frac{2 s ( - s ^{2} + 3 )}{( s ^{2} + 1 ) ^{3}}

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