derivative ((s+2))/((s^2+4s+13))

解

導関数

\frac{( s + 2 )}{( s ^{2} + 4 s + 13 )}

\frac{- s ^{2} - 4 s + 5}{( s ^{2} + 4 s + 13 ) ^{2}}

解答ステップ

\frac{d}{d s} (\frac{s + 2}{s ^{2} + 4 s + 13})

商の法則を適用:

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

= \frac{\frac{d}{d s} ( s + 2 ) ( s ^{2} + 4 s + 13 ) - \frac{d}{d s} ( s ^{2} + 4 s + 13 ) ( s + 2 )}{( s ^{2} + 4 s + 13 ) ^{2}}

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

\frac{d}{d s} (s^{2} + 4 s + 13) = 2 s + 4

= \frac{1 \cdot ( s ^{2} + 4 s + 13 ) - ( 2 s + 4 ) ( s + 2 )}{( s ^{2} + 4 s + 13 ) ^{2}}

簡素化

\frac{1 \cdot ( s ^{2} + 4 s + 13 ) - ( 2 s + 4 ) ( s + 2 )}{( s ^{2} + 4 s + 13 ) ^{2}} : \frac{- s ^{2} - 4 s + 5}{( s ^{2} + 4 s + 13 ) ^{2}}

= \frac{- s ^{2} - 4 s + 5}{( s ^{2} + 4 s + 13 ) ^{2}}