What is the derivative of ((s^2-4s+20))/((s+2)(s+4)) ?

The derivative of ((s^2-4s+20))/((s+2)(s+4)) is (10s^2-24s-152)/((s+2)^2(s+4)^2)

What is the first derivative of ((s^2-4s+20))/((s+2)(s+4)) ?

The first derivative of ((s^2-4s+20))/((s+2)(s+4)) is (10s^2-24s-152)/((s+2)^2(s+4)^2)

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derivative of

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

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

Solution steps

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

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 ) ( 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}}

Simplify

\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}}

\int (6 e^{- 0.1 x}) d x

\frac{d}{d x} (\frac{x ^{2} + 2 x - 3}{( x + 1 ) ^{2}})

x \to - 4 lim (\frac{x ^{2} - 6}{4 - x})

\frac{d}{d x} ((x^{3} + 3 x) (2 x + 4))

\int y y d y

What is the derivative of ((s^2-4s+20))/((s+2)(s+4)) ?
The derivative of ((s^2-4s+20))/((s+2)(s+4)) is (10s^2-24s-152)/((s+2)^2(s+4)^2)
What is the first derivative of ((s^2-4s+20))/((s+2)(s+4)) ?
The first derivative of ((s^2-4s+20))/((s+2)(s+4)) is (10s^2-24s-152)/((s+2)^2(s+4)^2)