What is the derivative of (sqrt(s)-1)/(sqrt(s)+3) ?

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

What is the first derivative of (sqrt(s)-1)/(sqrt(s)+3) ?

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

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derivative of

\frac{s - 1}{s + 3}

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

Solution steps

\frac{d}{d s} (\frac{s - 1}{s + 3})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{y ^{3}}{x ^{2}})

\frac{\partial}{\partial y} (x^{5} y)

\int cos (2 t) e^{- s t} d t

\frac{d}{d x} (\frac{f ( x )}{x ^{4}})

\frac{\partial}{\partial x} (2 x - 3 cos (x) + 10 y)

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