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Beliebt Rechnen >

d/(ds)(2/(s^2+4))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral from 1 to 2 of x^2

\int_{1}^{2} x^{2} d x

integral from 0 to 2 of x/(sqrt(16-x^2))

\int_{0}^{2} \frac{x}{16 - x ^{2}} d x

integral of 5/(2x+7)

\int \frac{5}{2 x + 7} d x

limit as x approaches 2 of (x+4)/(3x-1)

x \to 2 lim (\frac{x + 4}{3 x - 1})

integral of 1/((4x^2-1)^2)

\int \frac{1}{( 4 x ^{2} - 1 ) ^{2}} d x