d/(ds)(k/(s^2+k^2))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int (x - 1) d x

t^{2} y^{^{''}} + 5 t y^{^{'}} - 12 y = 0

ma c l a u r in \frac{1}{( 1 - x ^{2} ) ^{2}}

10 x - 6 y x^{2} + 1 \frac{d y}{d x} = 0

\frac{d r}{d θ} = \frac{r ^{2} + 5 r θ ^{4}}{θ ^{5}}