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

The derivative of (sqrt(s)-2)/(sqrt(s)+4) is 3/(sqrt(s)(\sqrt{s)+4)^2}

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

The first derivative of (sqrt(s)-2)/(sqrt(s)+4) is 3/(sqrt(s)(\sqrt{s)+4)^2}

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derivative of

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

\frac{3}{s ( s + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{\frac{1}{2 s} ( s + 4 ) - \frac{1}{2 s} ( s - 2 )}{( s + 4 ) ^{2}} : \frac{3}{s ( s + 4 ) ^{2}}

= \frac{3}{s ( s + 4 ) ^{2}}

What is the derivative of (sqrt(s)-2)/(sqrt(s)+4) ?
The derivative of (sqrt(s)-2)/(sqrt(s)+4) is 3/(sqrt(s)(\sqrt{s)+4)^2}
What is the first derivative of (sqrt(s)-2)/(sqrt(s)+4) ?
The first derivative of (sqrt(s)-2)/(sqrt(s)+4) is 3/(sqrt(s)(\sqrt{s)+4)^2}