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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

\frac{2}{s + s ^{2} + 4} : - \frac{s - s ^{2} + 4}{2}

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Graph

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