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

Lösung

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

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

Schritte zur Lösung

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

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

Vereinfache

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

\frac{\partial}{\partial x} (x^{2 + 2 y^{2} + 3 z^{2}})

\int \frac{x + 4}{x ^{3} + x ^{2} - 2} d x

\frac{d}{d y} (x^{y^{z}})

d er i v a t i v e f (x) = \frac{5}{1 - 9 x}

d er i v a t i v e f (x) = 6 e^{x} + 4 x^{2}