d/(ds)((s^2-4s+20)/(s^2+6s+8))

解答

\frac{d}{d s} (\frac{s ^{2} - 4 s + 20}{s ^{2} + 6 s + 8})

\frac{10 s ^{2} - 24 s - 152}{( s ^{2} + 6 s + 8 ) ^{2}}

求解步骤

\frac{d}{d s} (\frac{s ^{2} - 4 s + 20}{s ^{2} + 6 s + 8})

使用微分除法定则:

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

= \frac{\frac{d}{d s} ( s ^{2} - 4 s + 20 ) ( s ^{2} + 6 s + 8 ) - \frac{d}{d s} ( s ^{2} + 6 s + 8 ) ( s ^{2} - 4 s + 20 )}{( s ^{2} + 6 s + 8 ) ^{2}}

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

\frac{d}{d s} (s^{2} + 6 s + 8) = 2 s + 6

= \frac{( 2 s - 4 ) ( s ^{2} + 6 s + 8 ) - ( 2 s + 6 ) ( s ^{2} - 4 s + 20 )}{( s ^{2} + 6 s + 8 ) ^{2}}

乘开

(2 s - 4) (s^{2} + 6 s + 8) - (2 s + 6) (s^{2} - 4 s + 20) : 10 s^{2} - 24 s - 152

= \frac{10 s ^{2} - 24 s - 152}{( s ^{2} + 6 s + 8 ) ^{2}}

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