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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

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

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

\int \frac{- 5 x ^{2}}{4 x - x ^{2}} d x

d er i v a t i v e f (x) = 8 x^{4} - 3 x^{3} + 4 x

\frac{d}{d x} (cos (sin (x^{4})))

\frac{d}{d y} (y^{1 - n})

\int \frac{2 x ^{2}}{4 + x ^{2}} d x