What is the derivative of (s^2-4)/(s+1) ?

The derivative of (s^2-4)/(s+1) is (s^2+2s+4)/((s+1)^2)

What is the first derivative of (s^2-4)/(s+1) ?

The first derivative of (s^2-4)/(s+1) is (s^2+2s+4)/((s+1)^2)

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derivative of

\frac{s ^{2} - 4}{s + 1}

\frac{s ^{2} + 2 s + 4}{( s + 1 ) ^{2}}

Solution steps

\frac{d}{d s} (\frac{s ^{2} - 4}{s + 1})

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 + 1 ) - \frac{d}{d s} ( s + 1 ) ( s ^{2} - 4 )}{( s + 1 ) ^{2}}

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

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

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

Simplify

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

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

\int \frac{1}{cos ( θ )} d θ

\int 2 y - x^{2} d x

y = \frac{1}{( 1 + x ^{2} ) , at ( - 1 , \frac{1}{2} )}

\int 3 x^{15} e^{- x^{8}} d x

\int 9 cos^{2} (3 θ) d θ

What is the derivative of (s^2-4)/(s+1) ?
The derivative of (s^2-4)/(s+1) is (s^2+2s+4)/((s+1)^2)
What is the first derivative of (s^2-4)/(s+1) ?
The first derivative of (s^2-4)/(s+1) is (s^2+2s+4)/((s+1)^2)