derivative s/(s^2+1)

Lösung

ableitung von

\frac{s}{s ^{2} + 1}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d s}{d s} = 1

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

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

1 \cdot (s^{2} + 1) - 2 ss = - s^{2} + 1

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

d er i v a t i v e - \frac{1}{( 2 x + 3 ) ^{\frac{3}{2}}}

\int 5 x^{3} (x - 5)^{- 4} d x

in v erse l a pl a ce \frac{s + 2}{( s - 1 ) ( s + 6 )}

a re a 2 x, x^{2} - 4 x

y^{^{'}} + 2 y = x^{2} + 2 x