Answer
The Derivative is:
$f'(s)=\frac{1}{\sqrt{s}(\sqrt{s}+1)^2}$
Work Step by Step
$f(s)=\frac{\sqrt{s}-1}{\sqrt{s}+1}$
Using Quotient Rule to find the Derivative:
$y'=\frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{g^2(x)}$
$f'(s)=\frac{(\frac{1}{2}\cdot \frac{1}{\sqrt{s}}-0)(\sqrt{s}+1)-(\sqrt{s}-1)(\frac{1}{2}\cdot \frac{1}{\sqrt{s}}+0)}{(\sqrt{s}+1)^2}$
$f'(s)=\frac{\frac{1}{2\sqrt{s}}(\sqrt{s}+1)-\frac{1}{2\sqrt{s}}(\sqrt{s}-1)}{(\sqrt{s}+1)^2}$
$f'(s)=\frac{\frac{1}{2\sqrt{s}}(\sqrt{s}+1-\sqrt{s}+1)}{(\sqrt{s}+1)^2}$
$f'(s)=\frac{\frac{1}{2\sqrt{s}}(2)}{(\sqrt{s}+1)^2}$
$f'(s)=\frac{\frac{1}{\sqrt{s}}}{(\sqrt{s}+1)^2}$
$f'(s)=\frac{1}{\sqrt{s}(\sqrt{s}+1)^2}$
