d/(ds)(s/(s^2+16))

Lösung

\frac{d}{d s} (\frac{s}{s ^{2} + 16})

\frac{- s ^{2} + 16}{( s ^{2} + 16 ) ^{2}}

Schritte zur Lösung

\frac{d}{d s} (\frac{s}{s ^{2} + 16})

Wende die Quotientenregel an:

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

= \frac{\frac{d s}{d s} ( s ^{2} + 16 ) - \frac{d}{d s} ( s ^{2} + 16 ) s}{( s ^{2} + 16 ) ^{2}}

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

\frac{d}{d s} (s^{2} + 16) = 2 s

= \frac{1 \cdot ( s ^{2} + 16 ) - 2 ss}{( s ^{2} + 16 ) ^{2}}

1 \cdot (s^{2} + 16) - 2 ss = - s^{2} + 16

= \frac{- s ^{2} + 16}{( s ^{2} + 16 ) ^{2}}

y^{^{'}} + cos (x) y = cos (x)

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in v erse l a pl a ce \frac{s + 3}{s ^{2} + 6 s + 10}

\frac{d}{d x} (5^{x} + 5 cos (\frac{5 x}{2}))

\int \frac{5 + t + t ^{2}}{t} d t