What is the derivative of ((s+2))/((s^2+4s+13)) ?

The derivative of ((s+2))/((s^2+4s+13)) is (-s^2-4s+5)/((s^2+4s+13)^2)

What is the first derivative of ((s+2))/((s^2+4s+13)) ?

The first derivative of ((s+2))/((s^2+4s+13)) is (-s^2-4s+5)/((s^2+4s+13)^2)

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derivative of

\frac{( s + 2 )}{( s ^{2} + 4 s + 13 )}

\frac{- s ^{2} - 4 s + 5}{( s ^{2} + 4 s + 13 ) ^{2}}

Solution steps

\frac{d}{d s} (\frac{s + 2}{s ^{2} + 4 s + 13})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d s} ( s + 2 ) ( s ^{2} + 4 s + 13 ) - \frac{d}{d s} ( s ^{2} + 4 s + 13 ) ( s + 2 )}{( s ^{2} + 4 s + 13 ) ^{2}}

\frac{d}{d s} (s + 2) = 1

\frac{d}{d s} (s^{2} + 4 s + 13) = 2 s + 4

= \frac{1 \cdot ( s ^{2} + 4 s + 13 ) - ( 2 s + 4 ) ( s + 2 )}{( s ^{2} + 4 s + 13 ) ^{2}}

Simplify

\frac{1 \cdot ( s ^{2} + 4 s + 13 ) - ( 2 s + 4 ) ( s + 2 )}{( s ^{2} + 4 s + 13 ) ^{2}} : \frac{- s ^{2} - 4 s + 5}{( s ^{2} + 4 s + 13 ) ^{2}}

= \frac{- s ^{2} - 4 s + 5}{( s ^{2} + 4 s + 13 ) ^{2}}

t^{2} \frac{d x}{d t} + 3 t x = t^{4} lo g_{10} (t) + 1

\frac{1}{x + x ln ( x )}

f (x) = (4 x^{2} + 3) (4 x - 5)

\frac{d}{d x} (ln (25))

x \to 0 lim (\frac{( 8 ^{x} - 1 )}{x})

What is the derivative of ((s+2))/((s^2+4s+13)) ?
The derivative of ((s+2))/((s^2+4s+13)) is (-s^2-4s+5)/((s^2+4s+13)^2)
What is the first derivative of ((s+2))/((s^2+4s+13)) ?
The first derivative of ((s+2))/((s^2+4s+13)) is (-s^2-4s+5)/((s^2+4s+13)^2)