What is the d/(ds)((3s^3+19s^2+41s+26)/((s+1))) ?

The d/(ds)((3s^3+19s^2+41s+26)/((s+1))) is (6s^3+28s^2+38s+15)/((s+1)^2)

What is the first d/(ds)((3s^3+19s^2+41s+26)/((s+1))) ?

The first d/(ds)((3s^3+19s^2+41s+26)/((s+1))) is (6s^3+28s^2+38s+15)/((s+1)^2)

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\frac{d}{d s} (\frac{3 s ^{3} + 19 s ^{2} + 41 s + 26}{( s + 1 )})

\frac{6 s ^{3} + 28 s ^{2} + 38 s + 15}{( s + 1 ) ^{2}}

Solution steps

\frac{d}{d s} (\frac{3 s ^{3} + 19 s ^{2} + 41 s + 26}{( s + 1 )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d s} ( 3 s ^{3} + 19 s ^{2} + 41 s + 26 ) ( s + 1 ) - \frac{d}{d s} ( s + 1 ) ( 3 s ^{3} + 19 s ^{2} + 41 s + 26 )}{( s + 1 ) ^{2}}

\frac{d}{d s} (3 s^{3} + 19 s^{2} + 41 s + 26) = 9 s^{2} + 38 s + 41

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

= \frac{( 9 s ^{2} + 38 s + 41 ) ( s + 1 ) - 1 \cdot ( 3 s ^{3} + 19 s ^{2} + 41 s + 26 )}{( s + 1 ) ^{2}}

Simplify

\frac{( 9 s ^{2} + 38 s + 41 ) ( s + 1 ) - 1 \cdot ( 3 s ^{3} + 19 s ^{2} + 41 s + 26 )}{( s + 1 ) ^{2}} : \frac{6 s ^{3} + 28 s ^{2} + 38 s + 15}{( s + 1 ) ^{2}}

= \frac{6 s ^{3} + 28 s ^{2} + 38 s + 15}{( s + 1 ) ^{2}}

\frac{\partial}{\partial x} (x sin (\frac{8}{x}))

x \to 0 lim (cos^{2} (x) \cdot x)

n = 0 \sum \infty \frac{1}{n + 16}

\frac{d ^{2} y}{d x ^{2}} + a \cdot y = 0

x \to 4 - lim (\frac{x - 4}{x - 3})

What is the d/(ds)((3s^3+19s^2+41s+26)/((s+1))) ?
The d/(ds)((3s^3+19s^2+41s+26)/((s+1))) is (6s^3+28s^2+38s+15)/((s+1)^2)
What is the first d/(ds)((3s^3+19s^2+41s+26)/((s+1))) ?
The first d/(ds)((3s^3+19s^2+41s+26)/((s+1))) is (6s^3+28s^2+38s+15)/((s+1)^2)