d/(ds)(3/(s^2+9))

Lösung

\frac{d}{d s} (\frac{3}{s ^{2} + 9})

- \frac{6 s}{( s ^{2} + 9 ) ^{2}}

Schritte zur Lösung

\frac{d}{d s} (\frac{3}{s ^{2} + 9})

Entferne die Konstante:

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

= 3 \frac{d}{d s} (\frac{1}{s ^{2} + 9})

Wende Exponentenregel an:

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

= 3 \frac{d}{d s} ((s^{2} + 9)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( s ^{2} + 9 ) ^{2}} \frac{d}{d s} (s^{2} + 9)

= - \frac{1}{( s ^{2} + 9 ) ^{2}} \frac{d}{d s} (s^{2} + 9)

\frac{d}{d s} (s^{2} + 9) = 2 s

= 3 (- \frac{1}{( s ^{2} + 9 ) ^{2}} \cdot 2 s)

Vereinfache

3 (- \frac{1}{( s ^{2} + 9 ) ^{2}} \cdot 2 s) : - \frac{6 s}{( s ^{2} + 9 ) ^{2}}

= - \frac{6 s}{( s ^{2} + 9 ) ^{2}}

cos^{2} (t) \frac{d y}{d t} = 1

\frac{d}{d x} (\frac{3 x - 1}{x})

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

\frac{d ^{2}}{d x ^{2}} (x^{2})

\int_{0}^{16} sin (x) d x