d/(ds)((s^2-4s+20)/((s+2)(s+4)))

解

\frac{d}{d s} (\frac{s ^{2} - 4 s + 20}{( s + 2 ) ( s + 4 )})

\frac{10 s ^{2} - 24 s - 152}{( s + 2 ) ^{2} ( s + 4 ) ^{2}}

解答ステップ

\frac{d}{d s} (\frac{s ^{2} - 4 s + 20}{( s + 2 ) ( s + 4 )})

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} - 4 s + 20 ) ( s + 2 ) ( s + 4 ) - \frac{d}{d s} ( ( s + 2 ) ( s + 4 ) ) ( s ^{2} - 4 s + 20 )}{( ( s + 2 ) ( s + 4 ) ) ^{2}}

\frac{d}{d s} (s^{2} - 4 s + 20) = 2 s - 4

\frac{d}{d s} ((s + 2) (s + 4)) = 2 s + 6

= \frac{( 2 s - 4 ) ( s + 2 ) ( s + 4 ) - ( 2 s + 6 ) ( s ^{2} - 4 s + 20 )}{( ( s + 2 ) ( s + 4 ) ) ^{2}}

簡素化

\frac{( 2 s - 4 ) ( s + 2 ) ( s + 4 ) - ( 2 s + 6 ) ( s ^{2} - 4 s + 20 )}{( ( s + 2 ) ( s + 4 ) ) ^{2}} : \frac{10 s ^{2} - 24 s - 152}{( s + 2 ) ^{2} ( s + 4 ) ^{2}}

= \frac{10 s ^{2} - 24 s - 152}{( s + 2 ) ^{2} ( s + 4 ) ^{2}}