What is the d/(ds)((s^2-4s+20)/(s^2+6s+8)) ?

The d/(ds)((s^2-4s+20)/(s^2+6s+8)) is (10s^2-24s-152)/((s^2+6s+8)^2)

What is the first d/(ds)((s^2-4s+20)/(s^2+6s+8)) ?

The first d/(ds)((s^2-4s+20)/(s^2+6s+8)) is (10s^2-24s-152)/((s^2+6s+8)^2)

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\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}}

Solution steps

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

Apply the Quotient Rule:

(\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}}

Expand

(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}}

\frac{d}{d x} ((x - 3)^{3} + 3 (x - 3)^{2} + 6)

7 arcsin (x^{3})

y = (4 t - 1) (6 t - 3)^{- 1}

\int \frac{4 x ^{4} + x + 1}{x ^{5} + x ^{4}} d x

ln (225 sin^{2} (x))

What is the d/(ds)((s^2-4s+20)/(s^2+6s+8)) ?
The d/(ds)((s^2-4s+20)/(s^2+6s+8)) is (10s^2-24s-152)/((s^2+6s+8)^2)
What is the first d/(ds)((s^2-4s+20)/(s^2+6s+8)) ?
The first d/(ds)((s^2-4s+20)/(s^2+6s+8)) is (10s^2-24s-152)/((s^2+6s+8)^2)