Find a formula for the derivative of the function
![\[ f(x) = \frac{\sqrt{x}}{1+x} \qquad x > 0. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-02161eaff377f50dc4a155c8c6311335_l3.png "Rendered by QuickLaTeX.com")
Using the formula for the derivative of a rational power of 
and the quotient rule for derivatives, we have
![\begin{align*} f'(x) &= \frac{\frac{1}{2}x^{-\frac{1}{2}}(1+x) - \sqrt{x}}{(1+x)^2} \\[8pt] &= \frac{1+x - 2x}{2 \sqrt{x} (1+x)^2} \\[8pt] &= \frac{1-x}{2\sqrt{x} (1+x)^2} \end{align*}](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-60508181cc218ed25c10e5aa13233b30_l3.png "Rendered by QuickLaTeX.com")
for 
.
Find a formula for the derivative of the function
Using the formula for the derivative of a rational power of and the quotient rule for derivatives, we have
for .
where does that 2x in the second line come from? thanks