What is the derivative of (sqrt(s)-5)/(sqrt(s)+1) ?

The derivative of (sqrt(s)-5)/(sqrt(s)+1) is 3/(sqrt(s)(\sqrt{s)+1)^2}

What is the first derivative of (sqrt(s)-5)/(sqrt(s)+1) ?

The first derivative of (sqrt(s)-5)/(sqrt(s)+1) is 3/(sqrt(s)(\sqrt{s)+1)^2}

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derivative of

\frac{s - 5}{s + 1}

\frac{3}{s ( s + 1 ) ^{2}}

Solution steps

\frac{d}{d s} (\frac{s - 5}{s + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d s} ( s - 5 ) ( s + 1 ) - \frac{d}{d s} ( s + 1 ) ( s - 5 )}{( s + 1 ) ^{2}}

\frac{d}{d s} (s - 5) = \frac{1}{2 s}

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

= \frac{\frac{1}{2 s} ( s + 1 ) - \frac{1}{2 s} ( s - 5 )}{( s + 1 ) ^{2}}

Simplify

\frac{\frac{1}{2 s} ( s + 1 ) - \frac{1}{2 s} ( s - 5 )}{( s + 1 ) ^{2}} : \frac{3}{s ( s + 1 ) ^{2}}

= \frac{3}{s ( s + 1 ) ^{2}}

\int t^{2} sin (5 t) d t

\frac{d}{d n} ((1 + i)^{n} + (1 - i)^{n})

\frac{d}{d x} (\frac{4}{x} - \frac{1}{x ^{3}})

\int_{1}^{3} f (2 x) d x

t \to 0 lim (ln (t + 1))

What is the derivative of (sqrt(s)-5)/(sqrt(s)+1) ?
The derivative of (sqrt(s)-5)/(sqrt(s)+1) is 3/(sqrt(s)(\sqrt{s)+1)^2}
What is the first derivative of (sqrt(s)-5)/(sqrt(s)+1) ?
The first derivative of (sqrt(s)-5)/(sqrt(s)+1) is 3/(sqrt(s)(\sqrt{s)+1)^2}