d/(ds)(((13(s+2)(s+5)))/((s(s+3))))

解答

\frac{d}{d s} (\frac{( 13 ( s + 2 ) ( s + 5 ) )}{( s ( s + 3 ) )})

\frac{13 ( - 4 s ^{2} - 20 s - 30 )}{s ^{2} ( s + 3 ) ^{2}}

求解步骤

\frac{d}{d s} (\frac{( 13 ( s + 2 ) ( s + 5 ) )}{( s ( s + 3 ) )})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 13 \frac{d}{d s} (\frac{( s + 2 ) ( s + 5 )}{s ( s + 3 )})

使用微分除法定则:

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

= 13 \cdot \frac{\frac{d}{d s} ( ( s + 2 ) ( s + 5 ) ) s ( s + 3 ) - \frac{d}{d s} ( s ( s + 3 ) ) ( s + 2 ) ( s + 5 )}{( s ( s + 3 ) ) ^{2}}

\frac{d}{d s} ((s + 2) (s + 5)) = 2 s + 7

\frac{d}{d s} (s (s + 3)) = 2 s + 3

= 13 \cdot \frac{( 2 s + 7 ) s ( s + 3 ) - ( 2 s + 3 ) ( s + 2 ) ( s + 5 )}{( s ( s + 3 ) ) ^{2}}

化简

13 \cdot \frac{( 2 s + 7 ) s ( s + 3 ) - ( 2 s + 3 ) ( s + 2 ) ( s + 5 )}{( s ( s + 3 ) ) ^{2}} : \frac{13 ( - 4 s ^{2} - 20 s - 30 )}{s ^{2} ( s + 3 ) ^{2}}

= \frac{13 ( - 4 s ^{2} - 20 s - 30 )}{s ^{2} ( s + 3 ) ^{2}}

d er i v a t i v e \frac{5}{( 1 + 3 x )}

\frac{d}{d t} (- 38 t + 220)

d er i v a t i v e (x^{2} + 9) (x^{3} + 5)

d er i v a t i v e \frac{( x ^{4} + 9 )}{x ^{2}}

d er i v a t i v e tan^{- 2} (x)